Remove chicken breasts from refrigeration 20 minutes before cooking. Pat completely dry with paper towels. Slice larger breasts horizontally to create even thickness (approximately 3/4 inch).
In a small bowl, combine 1 1/2 teaspoons kosher salt, garlic powder, onion powder, and black pepper. Drizzle chicken with 2 tablespoons olive oil, then apply seasoning mixture evenly on both sides.
Fill a large bowl with ice and water for an ice bath. Set aside.
Bring a large pot of water to a rolling boil. Add 1 tablespoon salt to the water. Add broccoli florets and blanch for precisely 2 minutes. Immediately transfer to ice bath using a slotted spoon. Cool completely for 2-3 minutes.
Remove broccoli from ice bath and spread on clean kitchen towels or paper towels. Pat dry thoroughly to remove excess moisture.
Heat a 12-inch skillet over medium-high heat. Add 1 tablespoon olive oil and swirl to coat. Place chicken in skillet without overcrowding (work in batches if necessary). Sear for 4-5 minutes until golden brown, then flip.
Reduce heat to medium, continue cooking for 4-6 minutes more, or until internal temperature reaches 165°F (74°C) at thickest part. Transfer to cutting board and allow to rest for 5 minutes before slicing.
In a bowl, combine remaining 1 tablespoon olive oil, minced garlic, lemon zest, 1 tablespoon lemon juice, red pepper flakes (if using), and 1/2 teaspoon kosher salt.
Return skillet to medium heat. Add broccoli and finishing sauce, tossing quickly for 1-2 minutes until heated through but still firm.
Cut chicken against the grain into 1/2-inch slices.
Divide chicken and broccoli evenly among 5 containers. Allow to cool completely before sealing lids.