In a shallow dish, whisk together the flour, salt, black pepper, and garlic powder.
Pat the chicken thighs dry and dredge each piece in the seasoned flour to coat evenly, shaking off excess.
Heat the olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken thighs to the skillet (work in batches if needed) and cook 2–3 minutes per side until golden brown; transfer the browned chicken to a plate.
Reduce heat to medium, add the pressed garlic to the skillet, and cook about 30 seconds until fragrant.
Pour in the balsamic vinegar, chicken broth, and honey, scraping up any browned bits from the pan and stirring to combine.
Stir in the diced roma tomatoes and bring the sauce to a simmer over medium heat.
Return the chicken thighs to the skillet, cover, reduce heat to low, and simmer 3–4 minutes until the chicken reaches 165°F (74°C) internal temperature.
Add the baby spinach, cover again, and cook 2–3 minutes until wilted and the chicken is cooked through.
Serve the chicken and sauce topped with shaved Parmesan cheese.