Heat a large saucepan or a pot and add the olive oil and pork. Let the pork brown from one side and flip to brown from the other (about 7 minutes total).
Add the mushrooms and stir until they water out completely and start to caramelize (about 7 minutes).
Reduce heat and add the onion, the garlic cloves (whole), bay leaves, cumin, all spice and thyme. Cook until the onion is soft and translucent, about 5 minutes.
Add the wine, salt and pepper and simmer covered, under very low heat, for 50 minutes or until tender.
Add the peppers and continue cooking covered for another 20 minutes or until pork is very tender and soft and the sauce has reduced and thickened.
Check the stew every now and then. If the sauce has reduced and thickened but the meat isn't ready yet, add a bit of hot water and continue cooking.