Adovada: Place the pork medallions in a shallow pan. Add olive oil (or vegetable oil), red chili powder, salt, garlic powder, cumin, and a dash of Worcestershire sauce. Cover and refrigerate for at least 1 hour, up to 24 hours. Chile Caribe: Preheat the oven to 350 degrees F.
De-seed the chiles and put on a baking sheet. Bake for 1 to 2 minutes until skin starts to blister and they begin to toast. Remove from the oven and put into pot of water with salt, garlic, cumin, bring to a boil and boil for 5 to 10 minutes. When done add the chiles to a blender, using the water you boiled them in, and blend to a smooth consistency. Return to the saucepan and simmer over low heat.
Beans: Cook the beans in either a pressure cooker or slow cooker until tender, about 1 hour or so in a pressure cooker. When done, add salt, vegetable oil (olive oil), and/or cumin.
Posole: Boil the posole (hominy) in a pressure cooker until done about 1 1/2 hours. Then add some red chile powder, thinly sliced onion, oregano, and salt. Boil for another 15 to 20 minutes.
Assembly: Preheat a grill to high.
Place the marinated pork medallions on the grill. Cook for about 2 minutes per side, this will cook quickly, don't overcook, you want to keep them moist inside.
Layer 3 pork medallions on a plate, ladle chile caribe over the pork and finish with the beans and posole. Serve with warm flour tortillas.