Step 1

Position a rack in lower third of oven; preheat to 425 degrees F.

Step 2

Cut each chicken breast in half crosswise on the diagonal into 2 roughly equal portions and sprinkle with 1/4 teaspoon each salt and pepper. Place flour in a shallow dish and dredge chicken lightly; reserve the remaining flour. Heat 2 tablespoons oil in a large skillet over medium heat. Add the chicken, skinned-side down; cook until browned on the bottom, about 6 minutes. Transfer, skinned-side up, to a rimmed baking sheet. Reserve the skillet.

Step 3

Toss broccolini with the remaining 2 tablespoons oil, half the garlic and 1/4 teaspoon salt. Spread out on the other half of the baking sheet.

Step 4

Roast until the broccolini is tender and an instant-read thermometer inserted into the thickest part of the chicken registers 165 degrees F, 15 to 20 minutes.

Step 5

Meanwhile, whisk 4 teaspoons of the reserved flour and wine in a small bowl until combined. Place the skillet over medium heat, add the remaining garlic and cook, stirring, for 30 seconds. Add broth; bring to a boil over high heat. Add the wine mixture and cook, stirring frequently, until thickened and reduced to about 1 cup, 4 to 5 minutes. Add Parmesan, 1 teaspoon thyme and the remaining 1/4 teaspoon each salt and pepper.

Step 6

To serve, divide the chicken, broccolini and rice among 4 dinner plates. Spoon the sauce over the chicken and sprinkle with the remaining 1 teaspoon thyme.