Roast Chicken with Sauce Chasseur

Name: Roast Chicken with Sauce Chasseur
Ingredients: 1 tablespoon grapeseed or other neutral oil; 4 (8-ounce) skin-on airline chicken breasts or boneless skinless chicken breasts; 1 1/2 teaspoons kosher salt, plus more to taste; 1/2 teaspoon black pepper; 4 large shallots, halved lengthwise, root ends trimmed; 8 thyme sprigs; 1/2 cup dry white wine (such as Aligoté or lightly oaked Chardonnay); 2 cups lower-sodium chicken broth; 2 tablespoons unsalted butter; 8 ounce fresh wild mushrooms, cleaned and cut into bite-size pieces (about 3 cups); 1/2 cup heavy cream; 1 large plum tomato, chopped; 1 tablespoon finely chopped fresh chives; 1 tablespoon finely chopped fresh tarragon