On a plate, combine 1 1/2 tbsp of flour, 1 tsp each of salt and pepper; add chicken and turn to coat.

Heat oil in a large nonstick skillet over medium-high heat. Add chicken and cook, turning as needed, until lightly browned and cooked through, about 5 minutes; remove to a plate.

Put 1 cup of broth and garlic in same skillet; bring to a boil over high heat, scraping up browned bits from bottom of pan with a wooden spoon. Add broccoli; cover and cook 1 minute.

In a small cup, stir together remaining 1/2 cup of broth, 1/2 tbsp of flour, and 1/4 tsp of salt; add to skillet and bring to a simmer over low heat.

Cover and cook until broccoli is crisp-tender and sauce is slightly thickened, about 1 1/2 minutes. Stir in chicken and lemon zest; heat through.

Remove skillet from heat and stir in parsley and lemon juice; toss to coat.