Add 1 teaspoon of flour to a small bowl, and remaining flour to a shallow dish.
Season both sides of chicken with salt and pepper, then dredge through the shallow dish, until well-coated in flour.
Melt 1 tablespoon butter in a large skillet over medium-high heat. Add 1 tablespoon Lemon EVOO to the pan, swirl to coat.
Add chicken to the pan, sautéing for about 4 minutes on each side or until done. Remove chicken from pan; keep warm.
Heat remaining 1 tablespoon LEMON EVOO to the pan; swirl to coat. Add shallots and sauté about 3 minutes, stirring frequently. Add sliced garlic and continue to saute for 1 minute, stirring constantly.
Add the wine and lemon juice and bring to a boil, scraping the pan to loosen browned bits. Cook until liquid almost evaporates, stirring occasionally.
Add 1/4 cup chicken broth to reserved 1 teaspoon flour; stir until smooth. Set aside.
Add chicken broth to pan and bring to a boil, cooking until reduced by half (about 5 minutes).