Meanwhile, heat the remaining 1 tablespoon oil in a medium skillet over medium heat. Add shallots and the remaining 1 teaspoon thyme and cook, stirring occasionally, until softened, about 2 minutes. Add cherries and cook, stirring occasionally, until the cherries are softened, 3 to 6 minutes. Stir in wine and increase the heat to high; cook for 1 minute. Remove pan from heat and stir in basil and the remaining 1/4 teaspoon salt.