PREHEAT oven to 375° F.
COMBINE flour, baking powder and salt in small bowl. Beat butter, peanut butter, granulated sugar, brown sugar and vanilla extract in large mixer bowl until creamy. Add eggs, one at a time, beating well after each addition. Gradually beat in flour mixture. Stir in morsels and oats. Drop by rounded tablespoon onto ungreased baking sheets.
BAKE for 10 to 12 minutes or until light golden brown. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely.
For larger cookies, drop dough by 1/4 cup amounts about 3 inches apart onto ungreased baking sheets. Bake for 12 minutes or until golden brown. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely. Makes about 24 cookies.