Cut each thigh into 2-3 medium pieces, then heat the butter well in a Dutch oven or a heavy-bottomed pan and cook them.
Make sure they don't sit too close to each other while frying, it's better to cook them in 2 rounds.
Toss the onion/shallots and the garlic cut into large pieces over the browned thighs.
Mix well and leave for another 5 minutes to cook.
Now season the meat with salt, ground pepper, bay leaf (and thyme if available).
Pour enough cold water to completely cover the meat, and add the wine if using.
Leave the pot over heat until the whole mixture starts to boil actively.
Then move to the preheated oven at 160°C. Cover with a lid or foil and bake for 2 hours.
After 1 hour, flip the meat.
After the full 2 hours, it will be perfectly baked. It's also very important that the juice doesn't drop too much. So, cook with a lid on and over medium heat.
Discard the bay leaf and the sprig of thyme, if using.
While it's hot, tear the meat into fine shreds using 2 forks.
Move the rillettes into bowls or small jars and press well with a spoon.
If it's not greasy enough, pour a few tablespoons of hot vegan butter on top.
Cover with a lid or cling film and refrigerate for at least 2 days.