Preheat oven to 350 degrees. In the bowl of a food processor, pulse flour, salt, and baking powder to combine. Add shortening, and pulse until mixture resembles coarse meal. With the machine running, gradually add beet, carrot, parsley, or tomato mixture (or 1/2 cup to 3/4 cup cold water for no added color) until dough comes together, about 1 minute.
Transfer dough to a very lightly floured work surface. Shape into a smooth rectangle, about 4 by 6 inches. Wrap in plastic and let dough rest in the refrigerator for 30 minutes. Roll out dough to an 8-by-10-inch, 1⁄4-inch-thick rectangle. Cut lengthwise into 1/4-inch-wide strips.
Using your hands, gently roll each strip back and forth to form 14-inch-long sticks. Arrange them on 2 baking sheets, side by side but not touching. (press ends onto baking sheet to keep sticks straight while they bake.) Bake until firm and cooked through, 18 to 20 minutes. Transfer sticks to a wire rack to cool.