Marinade: Puree shallots, lemongrass, ginger, 1/4 cup oil, lime juice, tamari, sugar, sea salt, pepper, and coriander in a blender until smooth.
Place chicken in a baking dish and spoon on marinade, rubbing it on all sides. Cover; chill 1/2 to 2 hours.
Heat 2 teaspoons oil in a medium saucepan over medium-high heat. Cook quinoa until toasted, 3 to 4 minutes.
Add broth; bring to a boil. Cover, reduce heat to medium-low and simmer until quinoa absorbs liquid, about 20 minutes. Turn off heat; let sit, covered, until ready to serve.
Heat a grill pan or skillet over high heat; coat with cooking spray. Cook chicken, turning once, for 4 minutes. Reduce heat to medium. Cook, turning once, until a meat thermometer reads 165 degrees, 10 to 12 minutes.
Remove chicken; let rest two minutes. Slice each breast on the diagonal into 1/2-inch pieces.
Heat remaining 1 tablespoon oil in a large skillet over medium-high heat. Cook sugar peas and peppers until crisp-tender, about 3 minutes. Season with salt and pepper. Turn off heat.
Add mint and toss. Divide quinoa among 4 plates. Top each with 1 sliced chicken breast and 1/4 of the vegetables.