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Mix flour, baking powder and salt in large bowl. Set aside. Beat butter and sugar in large bowl with electric mixer on medium speed until light and fluffy. Add egg, cream and vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Refrigerate at least 1 hour or until firm.
Preheat oven to 350°F. Mix peach preserves and ginger in small bowl. Set aside. Shape dough into 3/4-inch balls. Place 2 inches apart on parchment-lined baking sheets. Use a 1 teaspoon measuring spoon to make an indentation in center of each cookie. Fill indentations with peach preserve mixture (about 1/2 to 1 teaspoon each). Refrigerate cookie sheets 30 minutes before baking. (Refrigerate remaining dough while baking each batch of cookies.)
Bake 10 to 12 minutes or until lightly browned around the edges. Cool on baking sheets 1 minute. Remove to wire racks; cool completely. Store cookies in airtight container up to 5 days.