Start by seasoning the halved chicken breasts with sea salt, black pepper, and garlic powder. Dredge each piece in all-purpose flour, shaking off any excess.
In a large skillet, heat 3 tablespoons of olive oil and 3 tablespoons of butter over medium-high heat. Add the chicken in a single layer and cook for 4-5 minutes on each side until golden brown and cooked through. Remove and keep warm.
In the same skillet, add the chopped shallot and sliced baby bella mushrooms. Sauté for 3-4 minutes until mushrooms are tender and shallots are translucent.
Pour in the chicken stock and fresh lemon juice. Scrape the skillet bottom to deglaze and bring to a simmer.
Stir in the rinsed capers and baby kale. Cook for 2-3 minutes until kale is wilted and tender.
Return the cooked chicken to the skillet and simmer in the sauce for 2-3 minutes. Add the remaining 3 tablespoons of butter, stirring until melted and creamy.
Cook fettuccine pasta according to package instructions. Drain and add to the skillet with chicken and sauce, tossing to combine evenly.
Plate the pasta and garnish with coarsely chopped parsley if desired. Serve immediately.