Beat butter and sugar in bowl until creamy. Beat in egg and vanilla.
Sift flour, baking powder and salt into bowl. Stir flour mixture into butter mixture. Divide dough in half.
Place each dough half in separate bowls. Add pistachios, green coloring to one half. Mix red coloring and jam in small bowl; add to other half.
Place green dough on plastic wrap. Pat into 11 x 8-inch rectangle. Do same with red dough. Place red dough on top of green dough; peel off plastic wrap from red dough. Starting from a long side, roll up dough in plastic wrap into 11-inch-long cylinder. Chill 2 hours.
Heat oven to 375°F. Coat large baking sheet with nonstick cooking spray.
Unwrap dough. Using thin sharp knife, cut dough into 1/4-inch-thick slices. Place on baking sheet, spacing 1 inch apart.
Bake in 375°F oven 10 to 12 minutes, until edges just begin to color; don't overbake. Cool cookies on sheet on rack 5 minutes. Remove cookies to wire rack to cool completely.