Begin by patting the chicken breast cubes completely dry with a paper towel; this is crucial for getting a beautiful golden-brown sear. Season the chicken generously with half of the salt (½ teaspoon) and half of the black pepper (¼ teaspoon). Heat the olive oil in a large, deep skillet or Dutch oven over medium-high heat. Once the oil is shimmering, carefully add the chicken in a single layer. Be sure not to overcrowd the pan; cook in batches if necessary. Sear the chicken for 3-4 minutes per side, until it’s golden brown and cooked through. The goal here is to develop flavor through the Maillard reaction, so don’t be afraid of a nice brown crust. Once cooked, remove the chicken from the skillet with a slotted spoon and set it aside on a plate.

Reduce the heat to medium. To the same skillet, add the unsalted butter. Once it has melted, add the minced garlic and sauté for about 30-60 seconds, stirring constantly until it becomes fragrant. Be very careful not to let the garlic burn, as it will become bitter.

Sprinkle the all-purpose flour over the melted butter and garlic. Whisk constantly for about one minute. This process cooks out the raw flour taste and creates a paste known as a roux, which will thicken our sauce. Slowly, a little at a time, pour in the chicken broth while continuing to whisk vigorously. This slow addition is the key to preventing lumps. Once all the broth is incorporated and the mixture is smooth, bring it to a gentle simmer.

Allow the sauce to simmer for about 3-5 minutes, stirring occasionally. You will notice it begin to thicken slightly. Now, stir in the heavy cream, the remaining salt (½ teaspoon), the remaining black pepper (¼ teaspoon), the dried thyme, and the pinch of red pepper flakes if you’re using them.

Bring the sauce back to a gentle simmer. Add the uncooked potato gnocchi and the bite-sized broccoli florets directly into the skillet with the sauce. Stir gently to coat everything. Cover the skillet and let it cook for 5-7 minutes, or until the gnocchi are tender and have floated to the surface, and the broccoli is crisp-tender. The cooking time may vary slightly depending on the brand of gnocchi, so check the package instructions as a guide.

Uncover the skillet and reduce the heat to low. Stir in the freshly grated Parmesan cheese until it has completely melted into the sauce, making it even more luscious and cheesy. Return the cooked chicken and any accumulated juices from the plate back into the skillet. Stir everything together gently to combine, allowing the chicken to reheat in the warm sauce for a minute or two.

Taste the sauce and adjust the seasoning if necessary, adding more salt or pepper to your liking. Serve the creamy chicken and broccoli gnocchi hot, garnished with a generous sprinkle of fresh chopped parsley for a final touch of freshness and color.