Beat butter at medium speed with an electric mixer until creamy; gradually add sugars, beating well. Add egg and vanilla, beating until blended.
Combine flour and next 3 ingredients; gradually add to butter mixture, beating until blended. Stir in cranberries, pecans, and oats.
Drop dough by heaping tablespoonfuls 2" apart onto lightly greased baking sheets.
Bake at 375° for 9 to 11 minutes or until lightly browned. Cool on baking sheets 2 minutes. Transfer to wire racks to cool completely.
Microwave white chocolate and shortening in a medium-size microwave-safe bowl on HIGH 1 minute or until chocolate melts, stirring once. Dip half of each cookie into melted chocolate, letting excess drip back into bowl. Place dipped cookies on wax paper; let stand until firm.