Pour the warm water into a large mixing bowl and whisk in the yeast. Let it rest for about a minute to activate. Stir in the salt, brown sugar, and melted butter. Gradually incorporate 3 cups of flour, adding one cup at a time. Use a wooden spoon or a stand mixer fitted with a dough hook to mix until a thick dough forms. Add another 3/4 cup of flour and continue mixing until the dough is no longer sticky. If the dough still feels tacky, add an additional 1/4 to 1/2 cup of flour, a little at a time. The dough is ready when it springs back when gently pressed with a finger.
Transfer the dough to a lightly floured surface and knead for 5 minutes, or continue kneading with the mixer for the same duration. If the dough becomes too sticky while kneading, sprinkle a teaspoon of flour at a time over the surface or the dough itself, ensuring it remains soft and pliable without becoming dry. After kneading, the dough should be smooth and slightly elastic. To check if it’s kneaded enough, perform the "windowpane test" by stretching a small portion until thin—if light passes through without tearing, the dough is ready.
Shape the dough into a ball and cover it with a clean kitchen towel. Let it rest for 10 minutes. Meanwhile, bring a large pot of water and baking soda to a boil.
Preheat the oven to 400°F (204°C). Line two baking sheets with silicone baking mats or lightly greased parchment paper for best results.
Divide the dough into equal portions, about 1/3 cup each (approximately 75g per piece). Roll each portion into a rope about 20–22 inches long. To shape a pretzel, form a circle by bringing the ends together, then twist them once or twice before pressing the twisted ends down toward the base of the loop.
Carefully lower one to two pretzels at a time into the boiling baking soda bath, letting them cook for 20–30 seconds. Avoid exceeding this time to prevent a metallic taste. Use a slotted spatula to lift each pretzel out of the water, allowing excess moisture to drain before placing it onto the prepared baking sheet. Sprinkle generously with coarse salt. Repeat with the remaining dough. If desired, refrigerate the boiled pretzels for up to 24 hours before baking.
Bake for 12–15 minutes, or until they develop a deep golden brown color. Remove from the oven and serve warm with your favorite dipping sauce, such as spicy nacho cheese.
Store any leftover pretzels in an airtight container at room temperature for up to three days. To reheat, microwave briefly or warm them in a 350°F (177°C) oven for about 5 minutes. For long-term storage, refer to the make-ahead and freezing instructions in the recipe notes.