1. Season the chicken cutlets with salt and pepper, then dredge each piece in flour, shaking off any excess.
2. Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add the chicken cutlets and cook until golden brown and cooked through, about 3-4 minutes per side. Remove chicken from the pan and set aside.
3. In the same skillet, reduce heat to medium, add the minced garlic, and sauté until fragrant, about 1 minute.
4. Pour in the chicken broth and lemon juice, scraping up any browned bits from the bottom of the pan. Let the sauce simmer for 3-4 minutes to reduce slightly.
5. Stir in the capers and heavy cream, mixing well. Allow the sauce to simmer until it thickens to your liking.
6. Meanwhile, cook the spaghetti according to package instructions until al dente. Drain and set aside.
7. Return the chicken cutlets to the skillet, spooning some sauce over them to warm through.
8. To serve, plate the spaghetti and top with the chicken cutlets. Pour remaining creamy lemon sauce over the top. Garnish with chopped fresh parsley.