Season chicken with smoked paprika, kosher salt, and black pepper on both sides.
Heat 1 tablespoon oil in a large frying pan over medium-high heat.
Add chicken. Cook for 4 minutes each side or until browned. Transfer to a plate.
Melt 2 tablespoons of butter and 1 tablespoon of oil in a pan over medium-high heat.
Add the mushroom halves and cook, stirring, until golden brown, about 5 minutes. Remove mushrooms and set aside.
Add ¼ cup of Madeira wine or chicken stock to the pan, scraping up any brown bits.
Add the remaining 2 tablespoons of butter to the pan. Add the minced garlic and chopped tarragon. Cook for 1 minute or until fragrant.
Add the remaining ¼ cup of Madeira wine or chicken stock to the pan and cook for 1 minute.
Return the chicken and mushrooms to the pan. Cook, turning occasionally, for 10 minutes or until the chicken is cooked through. Season with kosher salt and pepper.
Turn the heat off the pan, add the baby spinach, cover, and let stand for 2 minutes, or until the spinach is wilted.
Serve immediately with your favorite salad and or side dish.