HEAT oven to 400°F.
COMBINE 1 1⁄2 cups sugar, shortening, eggs, milk and vanilla in bowl of electric mixer. Beat at medium speed until well blended.
COMBINE flour, cream of tartar, baking soda and salt in medium bowl. Add gradually to shortening mixture at low speed. Mix just until blended.
COMBINE remaining 1⁄2 cup sugar and cinnamon in small bowl. Shape dough into 1-inch balls. Roll in sugar-cinnamon mixture. Place 2 inches apart on ungreased baking sheets.
BAKE 7 to 8 minutes. Cool 2 minutes on baking sheets. Place on cooling racks to cool completely.
COLORED SUGAR SNICKERDOODLES: Add 2 teaspoons cinnamon to flour mixture in Step 3. Combine 3 tablespoons colored sugar and 3 tablespoons granulated sugar to use for coating instead of cinnamon-sugar mixture.
TIP - Cinnamon-sugar mixture can be put in resealable plastic food storage bag. Place 2 to 3 cookie dough balls at a time in bag. Seal. Shake to sugar-coat dough.