Place a rack in center of oven; preheat to 350°. In a medium heatproof skillet over medium heat, heat oil. Season chicken all over with ½ teaspoon salt and ¼ teaspoon pepper. Cook, undisturbed, until golden brown on the bottom, 6 to 8 minutes. Turn and cook until other side is golden brown, 6 to 8 minutes more.

Transfer pan to oven and bake until chicken is cooked through (an instant-read thermometer inserted into thickest part should register 165°), 5-10 minutes. Let cool at least 5 minutes, then transfer to a cutting board and slice ¼" thick. Increase oven temperature to 425°.

Meanwhile, in a medium heatproof bowl, season broccoli with remaining ¼ teaspoon salt. Pour 1 tablespoon water into bottom of bowl. Cover and microwave 1 minute. Stir and continue to microwave in 30-second increments until broccoli is bright green and fork-tender, 30 seconds to 1 minute more. Uncover and let cool slightly.

Lightly dust a work surface and a large metal baking sheet with flour. On floured surface, roll or stretch out dough to a 12" round. Transfer to prepared sheet. Top with Alfredo sauce, leaving a ½" border. Sprinkle with ½ cup Parmesan, then layer with broccoli and chicken. Top with mozzarella and remaining ½ cup Parmesan.

Bake pizza until golden brown underneath and cheese is melty on top, 20 to 25 minutes. Let cool 5 minutes, then top with more pepper, if desired.