Brush grill grates clean. Place vegetables directly on grates and grill until they begin to char and soften, about 8 to 10 minutes.
Transfer pepper to plastic bag to steam and cool.
Remove skins and seeds and coarsely chop; set aside. Coarsely chop tomato and onion.
Pulse almonds and garlic in a food processor until almonds are finely ground. Add vegetables, parsley, vinegar, capers and sugar; pulse 10 to 12 times, or until desired texture. Set aside. Bring to room temperature before serving.
Rinse and pat dry chicken. Place on plate and drizzle with 2 teaspoons oil, turning to coat. Sprinkle top side of chicken with approximately half the seasoning.
Grill, unseasoned side down, over direct medium-high heat for 5 to 7 minutes or until cooked through, turning once halfway through grilling. Sprinkle remaining seasoning on chicken.
Remove chicken to serving platter and let rest 5 minutes before serving.
Spoon ¼ cup romesco sauce on individual plate; top with grilled chicken breast and additional chopped parsley, if desired.
Store remaining romesco in the refrigerator for up to one week.