Rinse the rice if desired. In a medium saucepan, bring 3 cups water to a low boil, add 1 1/2 cups jasmine or basmati rice, stir, cover, reduce heat to the lowest setting, and cook for 10 minutes. Turn off the heat and let the rice sit, covered, for 20 minutes without lifting the lid. Fluff with a fork and stir in 2 tablespoons chopped basil and 2 tablespoons chopped cilantro.
Preheat the grill or grill pan to medium-high heat.
In a bowl, toss the chicken (1 lb) with 1 cup BBQ sauce, 2 tablespoons apricot preserves, and 1 tablespoon of the olive oil. If using skewers, thread chicken onto skewers; alternatively leave breasts whole.
Brush the peach halves with the remaining 1 tablespoon olive oil.
Grill the chicken 3–4 minutes per side, flipping gently 2–3 times, until cooked through and lightly charred. Grill peach halves about 2 minutes per side until tender. Grill the husked corn about 10 minutes, turning 2–3 times, until charred and tender.
Remove chicken, peaches, and corn from the grill and let rest 5 minutes.
In a bowl, combine 6 tablespoons softened butter, 1 teaspoon Worcestershire sauce, 1 teaspoon ancho chili powder, 1/2 teaspoon smoked paprika, 1/4 teaspoon cumin, 1/4 teaspoon cayenne, and a pinch of salt and pepper. Stir in 2 tablespoons chopped cilantro and 2 tablespoons chopped basil to make the herbed butter.
Shuck the grilled corn and rub the herbed butter all over each ear.
In a bowl, mash the 2 avocados and stir in the juice of 1 lemon, 1/2 cup chopped basil, a pinch of salt, then fold in 1/2 cup fresh berries until combined.
To assemble 4 bowls, divide the rice among bowls, top with equal portions of the grilled chicken, sliced peaches, buttered corn, a large dollop of the berry-smashed avocado, halved cherry tomatoes, and crumbled goat cheese. Serve immediately.