Place rabbit meat in a large bowl with a lid. Season with a teaspoon of salt and a teaspoon of pepper.Cover with onions, garlic, bell pepper, and thyme. Add the wine. Close with the lid and marinate for two hours in the refrigerator.
2. Separate
Remove the rabbit from the container, shaking off the excess liquid. Set aside the marinade mixture.
3. Cook
Heat the oil over medium-high heat in a heavy-bottom pot or dutch oven. Add the rabbit and cook stirring until it turns golden brown (careful with splatters!).
4. Braise
Add the bay leaf. Cover with a lid and lower temperature to medium heat. As the liquid evaporates, add water by the tablespoon, stirring frequently to prevent it from scorching.
5. Make sauce
Once the meat is cooked through and tender (approximately 40 minutes), let all the liquid evaporate. Stir in the peppers, onions, and thyme from the marinade (do not add the liquids yet), as well as the carrot and tomatoes. Cook stirring until the onion has become translucent.
6. Serve
Pour in the cooking wine from the marinade. Simmer over low heat until the sauce thickens. Season with salt and pepper to taste. Discard the bay leaf and thyme sprigs.Remove from the heat and serve.
Notes
If you want the sauce to be thicken, you can sprinkle a teaspoon of flour on the meat and cook stirring for a few seconds prior to adding the wine to it.