Heat 1 tablespoon of oil in a large skillet over medium heat. Season both sides of the chicken breasts with pepper, garlic powder, and 2 teaspoons of salt. Cook the chicken in the skillet until golden brown and cooked through, about 7 to 8 minutes per side. Transfer the chicken to a plate.
In a small bowl, combine cilantro, 1 cup of strawberries, 1/3 cup of jalapeños, 2 tablespoons of shallots, 1 tablespoon of vinegar, and 1/2 teaspoon of salt.
In the same skillet over medium heat, heat the remaining 1 tablespoon of oil. Cook the remaining jalapeños and shallots with a pinch of salt until softened, about 2 minutes. Add the remaining 1/2 cup of vinegar and deglaze the skillet, scraping the bottom. Stir in the chipotle chile, adobo sauce, BBQ sauce, honey, and remaining strawberries. Cook until the sauce thickens and the strawberries break down, about 7 to 8 minutes.
Return the chicken to the skillet to heat through. Spoon the strawberry salsa over the chicken and top with cilantro before serving.