1 ounce Parmigiano-Reggiano, finely grated (1/2 cup packed)
Steamed rice, for serving (optional)
Heat a large cast-iron skillet over medium-high. Season chicken with salt and pepper; dredge in flour, shaking off any excess. Add butter and 1 tablespoon oil to skillet. When butter melts, add chicken in a single layer and cook, flipping once, until golden brown in places but not cooked through, about 3 minutes. Transfer to a plate.
Add remaining 1 tablespoon oil, garlic, and thyme to skillet; cook until fragrant, 10 seconds. Stir in broth and cream cheese; cook until mixture boils and cheese melts. Add spinach and cook, stirring, until wilted, 2 to 3 minutes. Stir in artichokes; cook 1 minute more. Return chicken and accumulated juices to skillet. Simmer, shaking pan occasionally, until sauce is reduced and thickened slightly and chicken is just cooked through, about 3 minutes. Remove from heat; stir in lemon juice and cheese. Serve over rice.