Fill a large pot 3/4 of the way up with salted water; cover and heat to boiling on high. Wash and dry the zucchini; halve lengthwise, then thinly slice crosswise. Peel and roughly chop 2 cloves of garlic. Roughly chop the capers.

Meanwhile, add the pasta to the pot of boiling water. Cook, stirring occasionally, 8 to 10 minutes, or until al dente (still slightly firm to the bite). Turn off the heat. Reserving 1/2 cup of the pasta cooking water, drain thoroughly and return to the pot.

In the pan of reserved fond, heat a drizzle of olive oil on medium-high until hot. Add the sliced zucchini, Italian seasoning, and half the chopped garlic; season with salt and pepper. Cook, stirring occasionally, 3 to 4 minutes, or until lightly browned. Transfer to a bowl. Wipe out the pan.

In the same pan, heat a drizzle of olive oil on medium-high until hot. Add the chopped capers and remaining chopped garlic; season with salt and pepper. Cook, stirring constantly, 30 seconds to 1 minute, or until softened. Turn off the heat.

To the pot of cooked pasta, add the cooked zucchini, butter, crème fraîche, and half the reserved pasta cooking water. Cook on medium-high, stirring frequently, 1 to 2 minutes, or until combined and the pasta is coated (if necessary, gradually add the remaining cooking water to ensure the pasta is thoroughly coated). Turn off the heat. Taste, then season with salt and pepper if desired. Slice the cooked chicken crosswise. Serve the finished pasta topped with the sliced chicken and garlic-caper topping. Garnish with the cheese. Enjoy!