Melt 1 tablespoon butter in a medium saute pan over a medium heat and sauté 1 minced shallot about 2 minutes, just to soften.
Meanwhile in a bowl soak apricots in brandy and hot water until softened, about 10 minutes. Drain, reserving liquid.
In a food processor, add walnuts, rosemary, shallot and apricots, pulsing until coarsely chopped.
Spread about 1/4 cup of filling on breasts, leaving 1/4" space at edges. Roll breasts narrow side first and hold together with a toothpick or skewer.
Preheat oven to 350 degrees F.
Saute chicken rolls in a large pan with 1 tablespoon butter and olive oil over medium heat, about 2 minutes per side until golden brown on all sides. Transfer breasts to a baking dish.
Heat 1 tablespoon butter in pan, add remaining minced shallot and scrape browned bits, cooking for a minute or two, deglaze, sauté pan with reserved brandy from apricots.
Whisk in another 2 tablespoons of butter just until incorporated. Season to taste with salt and a dash of white pepper.
our sauce over chicken breasts.
Cover with foil and bake for an additional 15-20 minutes or until done, depending on thickness.