This is a difficult topic. Originally the peanut sauce came from Indonesia, without coconut milk. My earliest trials came from Sri Owens „Die indonesische Küche“ (The Indonesian Kitchen) in the middle of the 1970ies. Later I got a recipe of the peanut sauce with coconut from Thailand. Now I’m changing my peanut sauce between the Indonesian original to the Thailand copy how I want.
In earlier times I grated the peanuts with a food processor but that’s not really a good result. The sauce got not thick enough and you always have shreds in it. Now I’m using ready peanut butter, but with an eye on the ingredients.
The meat for the skewers: Indonesia is mainly muslimic, so the Saté kambing with lamb/mutton is the most common. Bali is mostly hindu and there they make the Saté babi with pork. The chicken variant is even a Thailand invention.
This post has the variants chicken and lamb, and the original Indonesian and Thailand version of the sauce. You are free to choose your own.

4 servings

Ingredients:
Chicken skewers or drumsticks:
800 g chicken breast or
1 kg chicken drumsticks
50 ml oil, sunflower or canola
100 ml Indonesian sweet soy sauce (ketjap manis)
1 small onion
1 large garlic clove
Peanut sauce:
200 g peanuts or
100 g peanut butter
1 tin of coconut cream, unsweetened
50 ml Indonesian soy sauce (ketjap manis)
20 g Terasi (Indonesian crab paste)
1 small onion
1 large garlic clove
1 teaspoon Sambal oelek

Preparation:
Cut the meat into thin strips. Place in a bowl. Cut the onion into rings, add. Chop garlic, add. Add soy sauce and oil. Marinate overnight. Stuck serpentine like on skewers. Grill approx. 5 minutes from each side, best on indirect heat so that the soy sauce gets not black.
Brown the peanuts in a pan without fat. Add the finely chopped onion, chopped garlic and the crumbled Terasi with a little oil in a pot. When the onion and garlic have adopted some color, add the coconut cream and simmer for about 1/4 hour. After that, add the soy sauce, sambal and peanuts and simmer for another 5 minutes until the sauce thickens.
Instead of using chicken breast on a skewer which also goes with chicken drumsticks.

Satay Kambing

4 servings

Ingredients:
1 chilli pepper
2 tablespoons Indonesian soy sauce (ketjap manis)
1 garlic clove
2 shallots
1 kg lamb leg or shoulder
1 recipe peanut sauce (see below)
1 onion

Preparation:
Cut lamb into bite-sized pieces. Peel the shallots and garlic, mince with soy sauce and chili in flash hacker. Pour over the meat, mix well and let stand overnight in the refrigerator. The next day, put on skewers and grill for about 5 minutes on each side. Arrange on a plate, pour with sauce. Peel the onion, cut into strips and sauté briefly in a pan. Pour over the skewers.
Serve with Asian cooked rice.

Peanut sauce

4 servings

Ingredients:
1 teaspoon brown sugar
1 garlic clove
2 shallots
120 g peanuts
10 g Terasi
chilli and salt to taste
1 tablespoon lemon juice
1 tablespoon vegetable oil
200 ml water

Preparation:
Fry crushed peanuts in oil. Crush shallots, garlic and Terasi, mix with chili and salt and sauté briefly in a little oil. Pour in the water. Once the water boils, add peanuts, lemon juice and sugar. Simmer bubbly, until the sauce thickens (takes about 5 minutes). Then season again with salt and chili.