1
Preheat the oven to 400°F.
2
In a small baking dish, toss the garlic cloves with the olive oil and a pinch of salt and pepper. Roast until fragrant and browned, about 20 minutes.
3
Transfer half of the roasted garlic to a medium pot along with the milk, parmesan, cream, 1/2 teaspoon salt and a pinch of white pepper. Bring to a simmer and cook for 10-15 minutes, until thickened, stirring often.
4
Arrange the chicken on a baking sheet, drizzle with olive oil and sprinkle with salt and pepper. Roast until cooked through, 15-20 minutes.
5
In a blender, combine the remaining roasted garlic, olive oil, red pepper flakes and lemon zest until smooth. Season to taste.
6
Bring a large pot of salted water to a boil for the broccoli. Prepare an ice bath by filling a large bowl with water and ice. When the water boils, add the broccoli for 2-4 minutes, until bright green and crisp-tender, then immediately use a slotted spoon to transfer the vegetables to the ice bath to stop the cooking process. Remove from the ice bath after 1-2 minutes. Toss the broccoli with the garlic-chile sauce. Season to taste with salt and pepper.
7
Return the large pot of salted water to a boil. Add the pasta and cook according to package instructions. Drain the pasta, return to the pot, and drizzle with olive oil to prevent sticking.
8
To serve, toss the pasta with the alfredo sauce, divide between plates, top with chicken breasts and broccoli.