In a large mixing bowl or the bowl of a stand mixer, stir together the warm water, light brown sugar, and 1 tablespoon honey. Sprinkle the active dry yeast over the top. Let sit for 5–10 minutes, until the mixture looks foamy and creamy on top. If it does not foam, discard and start again with fresh yeast and properly warmed water.

Add the melted butter and fine sea salt to the activated yeast mixture and stir to combine. Add 3 1/2 cups of the all-purpose flour and mix with a wooden spoon, spatula, or dough hook until a shaggy dough forms. Add the remaining 1/2 cup flour a little at a time until the dough pulls away from the sides of the bowl and feels soft but not sticky. You may need slightly less or slightly more flour depending on your kitchen conditions.

Turn the dough out onto a lightly floured surface and knead for 5–7 minutes, until smooth and elastic. Alternatively, knead with a stand mixer and dough hook on medium-low for 4–5 minutes. Shape the dough into a ball and place it in a lightly greased bowl, turning once to coat. Cover with a clean kitchen towel or plastic wrap and let rise in a warm spot for 45–60 minutes, or until doubled in size.

Near the end of the rising time, preheat the oven to 425°F (218°C). Line two large baking sheets with parchment paper or silicone baking mats. In a large deep pot, bring 10 cups of water and 2/3 cup baking soda to a gentle boil, stirring to dissolve the baking soda. Be aware that the mixture can foam, so use a deep pot.

Punch down the risen dough to release the air and transfer it to a lightly floured surface. Divide the dough into 4 equal pieces. Roll each piece into a rope about 18–20 inches long and about 3/4 inch thick. Using a sharp knife or bench scraper, cut each rope into 1–1 1/2 inch pieces to form pretzel bites. Arrange the pieces on the prepared baking sheets while you shape the remaining dough; they can be close together but not touching.

Working in batches of about 10–12 pieces at a time, carefully drop the pretzel bite dough pieces into the boiling baking soda water. Boil for 20–30 seconds, then use a slotted spoon to remove them, letting excess water drip off. Return the boiled bites to the prepared baking sheets, spacing them about 1 inch apart. Repeat with the remaining dough pieces.

In a small bowl, whisk together the egg and 1 tablespoon water to make an egg wash. Brush each pretzel bite lightly with the egg wash and immediately sprinkle with coarse kosher salt or pretzel salt. Bake at 425°F (218°C) for 12–15 minutes, rotating the pans halfway through, until the pretzel bites are a rich deep golden brown.

While the pretzel bites bake, prepare the glaze. In a small bowl, stir together the melted butter, honey, Dijon mustard, yellow mustard, and a pinch of cayenne pepper if using. Taste and adjust the flavors, adding more honey for sweetness or more Dijon for extra tang.

In another small bowl, whisk together the mayonnaise, Dijon mustard, honey, apple cider vinegar, and garlic powder until smooth. Season to taste with salt and black pepper. Adjust sweetness or tang by adding more honey or a splash more vinegar if desired. Refrigerate until ready to serve; it will thicken slightly as it chills.

When the pretzel bites come out of the oven, let them cool for about 5 minutes, then brush generously with the honey mustard butter glaze. Transfer to a serving platter and serve warm with the creamy honey mustard dip on the side.