How to Make It
To prepare chicken, cut each breast horizontally to, but not through, the other side to create a pocket. Lift top flap of chicken pocket; arrange 1/2 prosciutto slice in each pocket. Top each prosciutto slice with 1 cheese slice; press top flap of pocket down over filling. Heat a large skillet over medium-high heat. Add oil; swirl to coat. Sprinkle chicken with pepper. Add chicken to pan, top side down; sauté 5 minutes or until deeply browned. Turn and cook 4 minutes or until done. Remove from pan; keep warm.
Add shallots and thyme to pan; sauté 30 seconds, stirring constantly. Combine 2 tablespoons stock and flour in a small bowl, stirring with a whisk. Add flour mixture and remaining stock to pan. Bring to a boil; cook 3 minutes or until reduced to 3/4 cup, scraping pan to loosen browned bits. Remove from heat; stir in butter, parsley, and tarragon.
To prepare polenta, bring milk and 1/3 cup water to a simmer. Gradually add polenta, stirring constantly with a whisk. Cook 3 minutes or until thick, stirring constantly. Stir in 1/4 teaspoon salt. Serve polenta with chicken and gravy.