Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper to prevent sticking.
Slice the roll of sugar cookie dough in half. Place one half into a large zip-top bag. Add 3 tablespoons of flour and the red gel food coloring to the bag. Seal it tightly and knead the bag until the dough is evenly colored red. Set this red dough aside on your parchment-lined workspace.
Take the second half of the sugar cookie dough. Knead 3 tablespoons of flour directly into this dough until it's well combined. This will be your vibrant white dough.
Take about 1 tablespoon of the red dough and gently roll it between your palms to create a thin, long rope, about 7-8 inches in length. Repeat this step with 1 tablespoon of the white dough, making another thin rope of similar size.
Lightly moisten one side of the red dough rope with a tiny bit of water. Gently press the white dough rope against the moistened red rope. This helps them bond! Now, slowly roll both ropes together with the palm of your hand until they form one thicker, striped rope, approximately 1/2-inch thick and still about 7-8 inches long.
Carefully twist the combined red and white dough rope to create that beautiful spiral effect, just like a real candy cane. Gently transfer the shaped dough to your prepared baking sheet. Bend the top of the rope slightly to form the classic "hook" of a candy cane. Continue this fun process with the remaining red and white dough until all cookies are shaped.
Bake your candy cane cookies in the preheated oven for 8-12 minutes, or until the edges are just barely turning golden brown. Once baked, remove them from the oven and let them cool completely on the baking sheet before moving them to a serving platter. For an extra festive touch, sprinkle the platter with crushed candy canes before serving, if desired.