Beat butter at medium speed with an electric mixer until creamy; gradually add sugars, beating well. Add egg and vanilla, mixing well. Combine flour and next 3 ingredients; add to butter mixture, mixing well. Stir in oats, carrots, and pecans. Drop cookie dough by level tablespoonfuls onto ungreased baking sheets. Bake at 350 degrees for 10 minutes. Remove to wire racks to cool. Store in an airtight container up to 3 weeks or freeze up to 8 months.