Preheat oven to 400°F (200°C).
Toss halved baby potatoes with 2 tablespoons of olive oil, dried rosemary, salt, and pepper on a rimmed baking sheet.
Roast potatoes for 30 to 35 minutes, tossing halfway through, until golden brown and tender.
Season chicken thighs with salt, pepper, and smoked paprika.
Heat remaining 1 tablespoon of olive oil in a large skillet over medium-high heat; sear chicken for 6-7 minutes per side until internal temperature reaches 165°F (74°C).
Remove chicken from skillet and set aside; lower heat to medium and add butter to the same pan.
Sauté mushrooms for 5-6 minutes until moisture has evaporated and they are browned.
Add minced garlic and cook for 1 minute until fragrant.
Deglaze the skillet with chicken broth, scraping up browned bits, then stir in heavy cream.
Simmer the sauce for 5 minutes until thickened, then stir in Parmesan cheese and fresh thyme.
Return chicken to the skillet to coat in sauce and serve alongside the roasted potatoes.