Place duck breasts in a bowl. Add onion, garlic, adobo, peppercorns, and thyme; mix well. Marinate in the refrigerator for 2 hours.
Preheat the oven to 325 degrees F (165 degrees C).
Heat olive oil in a Dutch oven. Add tomato paste to hot oil; stir until bubbling, about 1 minute. Pour duck breast mixture into the Dutch oven. Add bell pepper. Cook until duck breasts are well browned, about 10 minutes per side.
Cover Dutch oven and transfer to the preheated oven. Bake until an instant-read thermometer inserted into the center reads at least 145 degrees F (63 degrees C), about 1 hour.
