Step 1

Preheat oven to 200 degrees. In a large pot, bring 4 quarts water and 1 tablespoon salt to boil.

Step 2

Add pasta and cook until al dente, about 9 minutes. Strain out pasta and reserve pasta cooking water.

Step 3

Return pasta cooking water to boil. Add broccoli and blanch until just tender and bright green, about 1 to 2 minutes. Immediately drain and plunge in to a bowl of ice water to stop the cooking and set the color.

Step 4

Meanwhile, arrange chicken on a baking sheet or work surface and sprinkle both sides generously with cajun seasoning.

Step 5

In large skillet, heat oil until shimmering. Arrange chicken in a single layer and cook, flipping once, until the temperature on an internal thermometer reaches 155 degrees, about 5 minutes on each side. Transfer clean baking sheet or oven-safe plate, cover with foil, and place in oven to keep warm.

Step 6

Clean skillet if desired (see notes). Return skillet to stove and melt butter until foaming over medium-high heat. Stir in garlic until fragrant, about 30 seconds.

Step 7

Whisk in wine to deglaze the pan. Simmer until sauce has reduced by half, about 2 minutes (your pan is hot at this point so it should go pretty quickly).

Step 8

Whisk in cream and simmer until slightly thickened, about 2 minutes. Fold in parmesan cheese. Season to taste with salt and pepper (I like 1 teaspoon salt and 1/2 teaspoon pepper).

Step 9

Return pasta to skillet and toss gently to coat. In skillet or in a large warmed bowl, pile broccoli on top of pasta, top with chicken, and garnish with more parmesan cheese.