In a large pot, bring salted water to a boil. Add the cubed potatoes and cook until tender, about 15-20 minutes. Drain and return to the pot.
While the potatoes are cooking, heat the olive oil in a large skillet over medium heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for 6-7 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 1 minute until fragrant. Pour in the chicken broth and heavy cream, stirring to combine. Add the dried thyme and bring to a simmer.
Return the chicken to the skillet, cover, and simmer for about 5 minutes until the sauce thickens slightly. Stir in the grated Parmesan cheese until melted and smooth.
For the mashed potatoes, add the butter and milk to the drained potatoes. Mash until smooth and creamy. Stir in the shredded cheddar cheese, and season with salt and pepper to taste.
Serve the creamy garlic chicken over a generous scoop of cheesy mashed potatoes. Garnish with chopped parsley.
Notes
For a lighter version, substitute half-and-half for heavy cream and use low-fat cheese.
Add steamed broccoli or green beans to the plate for a pop of color and extra nutrition.