Beat butter at medium speed with an electric mixer until fluffy; add powdered and granulated sugars, beating well. Add eggs, oil, vanilla, and lemon juice, beating until blended.
Combine flour and next 3 ingredients; gradually add to sugar mixture, beating until blended.
Shape dough into 1-inch balls, and place about 2 inches apart on lightly greased baking sheets.
Bake, in batches, at 350° for 9 to 11 minutes or until set. (Do not brown.) After baking, immediately place a miniature peanut butter cup in the center of each cookie. Remove to wire racks to cool.