For the pretzel dough: Combine the butter, brown sugar and 2 cups of warm water (110 to 115 degrees F) in the bowl of stand mixer fitted with a dough hook. Sprinkle the yeast over the water and let stand until foamy, about 10 minutes. Whisk together the flour and kosher salt in a medium bowl.
Add half of the flour mixture to the yeast mixture and begin to mix on low speed. Increase the speed to medium as the flour becomes incorporated (scrape down the sides of the bowl as needed). Reduce the speed to low and add the remaining flour. Increase the speed to medium again and continue to beat until the dough gathers around the hook and pulls away from the side of the bowl, about 3 minutes.
Turn the dough out onto a flour-dusted surface and knead by hand until smooth, about 5 minutes, using more flour as needed. Butter the inside of a large bowl; add the dough and turn it to coat all sides with the butter. Cover the bowl and let the dough rise in a warm spot until doubled in size, about 1 hour.
Line a baking sheet with parchment and generously spray with cooking spray. Punch down the dough and cut it into 10 equal pieces; cover with a towel.
Tape a 24-inch-long piece of string to the countertop. Roll out a piece of dough on the countertop with your hands, starting in the middle and working your way out to the ends until you have a 24-inch-long rope (the string will help you measure). As you roll, occasionally lift the dough by the ends and slap the middle against the counter to stretch it.
Lift the ends of the rope to make a U shape, then cross one end over the other twice to make a double twist in the middle. Fold down the ends and attach them to the bottom of the U, forming a pretzel shape. Transfer to the prepared baking sheet; repeat with the remaining dough. Cover loosely with plastic wrap and let stand at room temperature until slightly puffed, about 30 minutes.
For the everything bagel topping: Meanwhile, combine the minced garlic and onion, poppy and sesame seeds and coarse salt in a small bowl.
Position the oven racks in the upper and lower thirds of the oven; preheat the oven to 425 degrees F. Fill a wide pot with 10 cups water; add the baking soda and bring to a low simmer, whisking to dissolve. Use scissors to cut the parchment around each pretzel, leaving a 1-inch border. Slide the pretzels (on the parchment) off the baking sheet. Coat the baking sheet with cooking spray; coat a second baking sheet with spray. Working in batches, carefully invert each pretzel into the water, using tongs to peel off the parchment. Simmer until the pretzels plump, 30 to 45 seconds per side. Remove with a slotted spoon, letting the excess water drip off; arrange on the prepared baking sheets. Sprinkle with the everything bagel topping.
Bake the pretzels, rotating the baking sheets halfway through, until golden brown, 12 to 15 minutes. Brush with the melted butter and serve with the mustard.
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