Jarred red curry paste is the base of a flavorful, tangy mixture that serves double-duty as both marinade for chicken and finishing sauce for veggies. We use a combination of peppers for different flavor notes—mini bell peppers for sweetness and Fresnos for moderate spice. Fresnos look like red jalapeños but are less spicy; use the latter if you want more heat. Look for red curry paste and sambal oelek on the Asian foods aisle of your supermarket. For less chile heat, decrease or omit the sambal, and use all sweet peppers. Serve with brown rice to complete the meal.
Whisk together first 5 ingredients. Place chicken and half (about 1/3 cup) of the curry paste mixture in a large ziplock plastic bag. Reserve remaining mixture. Seal bag, removing any excess air, and massage mixture into chicken. Chill 2 to 24 hours, turning occasionally.
Preheat grill to medium-high (about 450°F).
Coat bell peppers, Fresno chiles, and shallots with cooking spray, and place in a single layer on grill grate. Grill bell peppers and Fresno chiles, uncovered, until charred, turning occasionally, 6 to 8 minutes. At the same time, grill shallots until charred, 2 to 3 minutes. Place bell peppers, Fresno chiles, shallots, and 2 tablespoons reserved curry paste mixture in a large bowl, and toss to coat.
Remove chicken from marinade; discard marinade in bag. Place chicken on grill grate, and grill, uncovered, until done, 5 to 6 minutes per side. Arrange vegetables and chicken on a platter; top with remaining curry paste mixture.