01 - Combine warm water and sugar in a small bowl. Sprinkle yeast on top and let stand for 5 minutes until foamy.
02 - Mix flour, salt, and cinnamon in a large bowl. Add yeast mixture and melted butter. Knead by hand or with mixer for 8-10 minutes until smooth and elastic.
03 - Divide dough evenly into three portions. Tint each portion with a different food coloring (purple, green, yellow), kneading until color is uniform throughout.
04 - Cover dough portions and let rest for 1 hour or until doubled in size.
05 - Roll each colored dough into ropes about 12 inches long. Twist one rope of each color together, then form into a bagel shape, pinching ends tightly to seal. Repeat for remaining dough.
06 - Place bagels on parchment-lined baking sheet. Cover and let rest for 20 minutes.
07 - Preheat oven to 425°F.
08 - Bring a large pot of water to boil. Add honey or sugar. Boil bagels, 2 at a time, for 1 minute per side. Remove and drain on wire rack.
09 - Place boiled bagels back on baking sheet. Bake for 18-22 minutes until golden brown. Cool completely.
10 - Whisk powdered sugar, milk, and vanilla until smooth. Drizzle over cooled bagels and immediately sprinkle with colored sugars.