Preheat oven to 450ºF with a rack in the center. Finely chop 1 teaspoon garlic. Trim stem ends from broccoli, then cut crowns into 1-inch florets. Finely grate all of the lemon zest into a medium bowl, then add chopped garlic, ½ teaspoon Italian seasoning, 3 tablespoons oil, ¾ teaspoon salt, and a few grinds of pepper.

Transfer half of the garlic-herb oil to a small bowl; reserve for step 6. Pat chicken dry and pound to an even ½-inch thickness, if necessary. Add chicken to bowl with remaining garlic-herb oil, tossing to coat. Let chicken marinate until step 5.

On a rimmed baking sheet, toss broccoli with 2 tablespoons oil and season with salt and pepper. Roast on center oven rack until broccoli is tender and browned in spots, 8–10 minutes (watch closely as ovens vary).

Scrape and discard marinade from chicken. Heat 1 tablespoon oil in a medium skillet over medium-high. Add chicken; cook, turning once, until browned and cooked through, 3–4 minutes per side. Squeeze 1 tablespoon lemon juice into a small bowl; whisk in honey, 1½ tablespoons water, and 2 teaspoons Dijon mustard; season with salt and pepper. Cut any lemon into wedges.

Remove skillet from heat; pour honey-Dijon dressing over chicken, tossing to coat. Drizzle reserved garlic-herb oil over broccoli. Serve chicken with broccoli alongside, and with any lemon wedges for squeezing over top. Enjoy!