Proof the yeast: In a large bowl, stir warm water with sugar.
Sprinkle yeast on top. Let it sit 5–10 minutes until foamy. If it doesn’t foam, start over with fresh yeast.
Make the dough: Add melted butter and salt to the yeast mixture.
Stir in 3 1/2 cups flour with a spoon. Add more flour, a little at a time, until the dough forms a soft ball that pulls from the sides. It should be slightly tacky but not sticky.
Knead: Turn dough onto a lightly floured surface.
Knead 5–7 minutes until smooth and elastic. Add sprinkles of flour as needed to prevent sticking, but keep it soft.
First rise: Place dough in a lightly oiled bowl. Cover and let rise in a warm spot for 45–60 minutes, or until doubled in size.
Preheat and prep: Heat oven to 450°F (232°C).
Line two baking sheets with parchment paper and lightly grease the parchment. In a large pot, bring 10 cups water and 2/3 cup baking soda to a gentle boil.
Divide and shape: Punch down the dough and divide into 12 equal pieces. Roll each piece into a rope about 14–16 inches long.
To form an egg twist, coil the rope into an oval spiral, tucking the end underneath. For a braided egg, use two shorter ropes, twist them together, and shape into an oval.
Baking soda bath: Working in batches, carefully drop each twist into the simmering baking soda water for 20–30 seconds. Use a slotted spatula to lift out, let excess water drip off, and place on prepared sheets.
Egg wash and salt: Brush each twist with egg wash.
Sprinkle with coarse salt if making classic pretzels. If you plan to glaze, skip the salt.
Bake: Bake 10–12 minutes until deep golden brown. Rotate pans halfway if your oven bakes unevenly.
Finish and decorate: For sweet versions, let pretzels cool 10 minutes, then dip or drizzle with colored glaze and add sprinkles.
For cinnamon sugar, brush warm pretzels with melted butter and toss in a sugar-cinnamon mix.
Serve: Enjoy warm. These are great plain, with mustard, or with a sweet dipping sauce like vanilla yogurt or cream cheese icing.