Season both sides of the chicken breasts generously with sea salt, black pepper, and garlic powder. Dredge each piece in flour, shaking off any excess.
In a large skillet over medium-high heat, add 3 tablespoons of butter and 3 tablespoons of olive oil. Heat until the butter is melted and bubbling. Carefully place the dredged chicken into the skillet, ensuring not to overcrowd the pan. Cook for about 3 minutes on each side until golden brown and cooked through. Transfer the chicken to a plate and cover to keep warm.
In the same skillet, add the shallot and mushrooms. Sauté for about 2 to 3 minutes until the shallot is translucent and the mushrooms are browned and fragrant.
Add the baby kale to the pan, stirring gently until it wilts. This should take about 1 to 2 minutes.
Pour in the chicken stock and let it simmer, allowing the flavors to meld together. Reduce the mixture by half, which takes around 3 minutes.
Lower the heat and stir in the remaining butter, capers, and lemon juice. Taste and adjust seasoning with more salt and pepper as needed.
Add the cooked fettuccine to the skillet, tossing to combine. The pasta should be well-coated in the sauce.
To serve, plate up the Creamy Chicken Picata Pasta and garnish with coarsely chopped parsley if desired.