While chicken is baking, make the pan sauce. In the same skillet used to brown the chicken, melt butter over medium heat. Add shallot and cook until soft, 3-4 minutes, stirring often. Add remaining garlic and cook until fragrant, about 2 minutes. Add wine and scrape up any brown bits from the bottom of the pan. Cook for 2 minutes. Add broth, cream, and remaining 1 tablespoon tarragon. Stir to combine. Cook, stirring occasionally, until sauce thickens, about 5 minutes. Taste and add salt and pepper as necessary.