Place the red bell pepper, cut side down, on an aluminum foil or parchment-lined baking sheet. Roast for 40 minutes, flipping both pieces over midway. The bell pepper will wilt and blacken.
Use a knife to cut 3-5 slits into each chicken piece and place in a large bowl
Add the roasted bell pepper, lemon juice, vinegar, oil, garlic, spice blend, sugar and salt to a food processor. Blend until as smooth as possible
Reserve 1/2-cup of the sauce, then pour the remaining sauce onto the chicken. Mix well to ensure the chicken is thoroughly coated. Cover and refrigerate for at least 2-3 hours, ideally overnight.
When ready to cook, take the chicken out of the fridge and allow it come closer to room temperature. Preheat the oven to 350°
Meanwhile, heat a large skillet or stovetop grill pan over medium-high to high heat. Once hot, brush or spray with oil and add the chicken pieces, meat side down. Discard any marinade that was in contact with the chicken, still keeping in reserve the marinade that has not been used. Grill the chicken, pressing down on it to increase grill marks, for 4 minutes each side, or until charred or browned on both sides.
Place the chicken pieces side by side in an oven-safe pan or roaster. Cover the pan tightly with aluminum foil and place the baking dish on the center rack of the oven. Roast for 20-25 minutes or until the chicken is cooked through. Bake time will depend on the cut of chicken. the smaller pieces will take around 20 minutes, medium size pieces (legs/thighs) will take around 22 minutes, and larger pieces (such as leg quarters) will take 25.
Meanwhile, mix unused marinade with mayonnaise. Taste and adjust salt or add more mayonnaise if needed. Brush the sauce over the chicken and serve hot.