In a large bowl, combine the chicken pieces with 1 tbsp olive oil, 1/2 tsp salt, and 1/4 tsp black pepper. Heat a large skillet over medium-high heat. Add the chicken and cook until browned and cooked through, about 5-7 minutes. Remove chicken from skillet and set aside.

In the same skillet (or a large pot if moving to soup), melt the 1/4 cup unsalted butter and 1 tbsp olive oil over medium heat. Add minced garlic, smoked paprika, dried oregano, dried thyme, and red pepper flakes. Sauté for 1 minute until fragrant. Stir in the chopped fresh parsley, lemon zest, remaining 1/2 tsp salt, and 1/4 tsp black pepper.

If not already in a large pot, transfer the cowboy butter mixture to a large pot or Dutch oven. Add the chopped onion, carrots, and celery. Cook over medium heat, stirring occasionally, until vegetables are softened, about 8-10 minutes.

If using flour for thickening, sprinkle the 2 tbsp all-purpose flour over the vegetables and stir for 1 minute. Gradually pour in the chicken broth, whisking constantly to prevent lumps if flour was added. Bring the soup to a boil, then reduce heat to a simmer, cover, and cook for 15 minutes.

Add the uncooked bowtie pasta to the simmering soup. Cook according to package directions, usually 8-10 minutes, or until al dente. Stir in the cooked chicken pieces.

Stir in the lemon juice and heavy cream (if using). Taste and adjust seasoning with additional salt and pepper as needed. Ladle the Cowboy Butter Lemon Bowtie Chicken Soup into bowls and garnish with extra fresh parsley, if desired.