Begin by making the Pappardelle and Vegetables: Cook the pappardelle according to the package directions until al dente. Drain well.
While the pasta cooks, make the veggies: In a large skillet, melt the butter and olive oil on medium heat. Add the carrots and snap peas and seasoning and cook until they're crisp tender, for about six minutes. Add the tossed pasta and pine nuts to the vegetables and cover to keep warm.
While the vegetables cook, make the Lemon Chicken with Capers: Slice each breast in half vertically, and pound them until they're a half inch thick. Season them with salt and pepper. Dip them lightly in the flour. In a cast iron skillet, heat the olive oil on medium heat. Fry a few pieces at a time until each breast is lightly browned on both sides. They only need to cook for a couple of minutes on each side. Remove them to a plate and cover them to keep warm.
Wipe out the pan. Melt two tablespoons of the butter in the pan and add the garlic. Cook on low heat for one minute. Add the lemon juice, white wine, and chicken stock. Simmer until reduced by half. Remove the pan from the heat.
Stir in the capers. Stir in the rest of the butter, one teaspoon at a time. Spoon the sauce over the chicken and top each piece with a lemon slice.