Two problems that occur during making vadai and ulundu vadai are the undercooked centers and them breaking during frying. Also a high oil temperature results in burnt vadai with undercooked centers.

To avoid these problems, arrange the vadai on a microwavable plate (not paper) at least 1/2 inch apart (usually 10 -15 vadai on a 9 inch dinner plate), microwave for about 3 minutes without a cover until the upper surface feels slightly firm and leathery. If the upper surface still feels soft microwave again until the surface feels firm. The time depends on the power of the oven. Then turn them upside down (the bottom side is usually soft still) and repeat the microwaving for a minute or two until this side feels firm. Total time for a plateful of vadai using a 1200 watt oven is usually 6 minutes.

Meanwhile have the wok ready with hot oil. Do not have the oil fuming hot as very hot oil will char the vadai. (my indicator or oil at right temperature is when a small piece of papadam puffs up immediately without browning). Fry the already microwaved vadai while they are still hot, about 3 - 4 at a time. Remove them when they turn golden brown. Vadai are usually already cooked after the microwaving. You are only browning the vadai and adding the flavor by frying.

Advantage of this technique:
1. No more undercooked centers or broken vadai. Also there is no oil splatter.
2. Every vadai comes out well irrespective of how watery your mixture/batter is.
3. You can achieve the desired color without undercooked centers.
4. This procedure works every time without failure and any amateur can do this.
5. Very little oil is absorbed into the vadai as the cooked surface prevents oil from entering the vadai.

You can prepare ulundu vadai in a similar fashion. However leave at least a 1 inch distance between the vadai as they expand more than regular vadai does.
If you make falafel (the Middle Eastern cousin of vadai using chick pea (garbanzo)) you could use the same technique. Be sure that you use fresh uncooked chick pea and not canned. I brown these on a flat pan. These also tend to absorb quite a bit of oil while vadai and ulundu vadai using the microwave technique do not absorb any or very little.

Recipe for vadai
Use your favorite recipe or the following;
1 lb (450 g) split peas (soaked at least for 6 hours) or 1 lb of masoor Dhal (soaked at least for 4 hours)
1 medium onion or 2 oz (60 g) shallots, chopped*
2-3 green chili peppers, chopped
Flaked red dried chili pepper to your liking (1-2 tea spoons)
Salt to taste
Two table spoons of thinly sliced Maldive Fish or dry shrimp/prawn powder (optional)
1 - 2 sprigs of curry leaves, thinly cut
About 2 cups of oil for frying

Wash the soaked lentils well and drain in a colander for about 10 minutes. Transfer this and the other ingredients (except oil) to a food processor (not a blender) and grind/process until about half of the lentils/peas have turned to a paste. You should be able to see some intact/partial grain at this stage.
Remove the mixture and make vadai to the desired size and first microwave cook as indicated above and then brown in hot oil. (Frying step is not more than a minute usually).

Recipe for ulundu vadai
You can use a store bought mixture/your favorite recipe or the following;
2 cups of urad dhal
5-6 green chillies (cut into small slices)
One medium onion or 3-4 shallots thinly cut.
Curry leaves from one to two sprigs thinly cut.
Salt to taste
Oil for frying

Method: Soak urad dhal for 3-4 hours. Wash and drain well. Process in a food processor (not a blender) until a paste is obtained. Remove from the food processor to a bowl and mix with the next four ingredients except the oil.

Make the ulundu vadai to the desired size and the donut shape. If the mixture is too sticky, you can add a bit of rice flour or garbanzo (chick pea) flour to make it less sticky and workable. Oiling the palm also makes this step a bit easy. Arrange in a microwavable plate as indicated above. Microwave them first until the upper side feels firm and leathery. Turn them upside down and microwave them until both sides feel firm/leathery.
Meanwhile have the oil hot in the wok. Brown the ulundu vadai until the desired color is obtained.

*I prefer shallots as these add very little moisture to the mixture and give a better aroma. Alternatively you could use the outer layers of two medium onions as they tend to have less water and a better aroma than the inner layers do. You could use the inner layers in fresh salads or mallun.