Preheat the oven to 400F. Arrange the tomatoes and onions on a baking sheet. Drizzle with olive oil and sprinkle with salt. Roast the vegetables for 20-30 minutes until wilted and darkened at the edges. Remove from the oven and leave the oven on.
Meanwhile, mix the parsley, garlic, sundried tomatoes, capers, and feta in a bowl with a fork to form a paste. Add 2 tablespoons of the butter to a large skillet and preheat to medium-high.
While the skillet is preheating, place the chicken breasts in a zipper bag and pound on the thick side to thin to about ¾ inch at the thickest place. Remove from the bag, and use a small knife to make a hole in the thickest part of the chicken breast. Wiggle the knife back and forth to make a pocket in the chicken. Use your fingers to stuff as much of the filling into the chicken breast as you can, then repeat with the other piece of chicken. Place the stuffed chicken breasts in the skillet you have been preheating.
Sprinkle the chicken with salt, and brown the chicken for about 5 minutes on each side until very golden. Transfer the chicken to a small baking dish and reduce the heat on the skillet to medium for the pan sauce.
Bake the chicken at 400F for 10 minutes to finish cooking. While the chicken is baking, pour the white wine into the skillet you used to sear the chicken. When the wine has reduced by half, add the remaining 2 tablespoons butter and the roasted onions and tomatoes. Stir to form a sauce and taste; add salt to your preference.
When the chicken and the sauce are done, slice the chicken and arrange it on a plate. Top with the roasted tomato sauce. Serve. Eat. Enjoy!