Reduce heat to medium. Add sherry or wine and deglaze pan for a minute or so. Add chicken broth and a couple tablespoons of pesto (to taste). Save remaining pesto (in an airtight container in the fridge) for other uses. Cook for another minute, stirring frequently. Add remaining tbsp of butter to enrich sauce. If needed, add a little more chicken broth (about 1/4-1/3 cup) to sauce. Add chicken back to pan and cook until chicken is cooked through, 2-4 minutes. Add capers and generous squeeze of lemon.