Using a small knife, make an incision in the top rounded end of a chicken breast, cutting through the center and to the ends without breaking the sides, to form a pocket for the stuffing.
Combine the tomatoes, ricotta, walnuts, sage and egg yolk in a small bowl and season with salt and pepper. Using a spoon (or place the filling into a piping bag without a tip), stuff one of the chicken breasts with half of the ricotta mixture. Seal the cut end of the chicken closed using a toothpick. Repeat with the other chicken breast.
Lay the prosciutto into 2 sheets (3 pieces each) and roll around each stuffed breast. Season the chicken with salt and pepper.
Heat the canola oil in a large, ovenproof saute pan until almost smoking. Sear the chicken breasts on the seam side of the prosciutto, then flip and transfer the pan to the oven. Roast until the center of the chicken registers 160 degrees F, 12 to 15 minutes.
Remove the chicken from the pan, add the capers and shallots and cook over medium-high heat for 1 minute to soften the shallots. Add the chicken stock and cook until reduced by half, then swirl in the butter. Add the parsley and lemon juice and season with salt and pepper.
Slice the chicken and serve with the sauce over the top.