Heat olive oil in a large skillet over medium-high heat.
Add chicken pieces and sear until browned and cooked through, approximately 8 to 10 minutes, then remove chicken from the pan and set aside.
In the same skillet, add the cauliflower florets and sauté for 6 minutes until slightly tender and golden on the edges.
Add minced garlic to the cauliflower and cook for 1 minute until fragrant.
Reduce heat to medium and pour in the heavy cream and dried thyme, bringing the mixture to a gentle simmer.
Stir in the grated Parmesan cheese until melted and the sauce has thickened.
Return the cooked chicken to the skillet and toss to coat with the cream sauce.
Season with salt and pepper to taste and simmer for an additional 2 minutes.
Garnish with fresh parsley before serving.