Rosemary Cheese Pretzels with Cheddar Dip

Ingredients

• 1 1/2 cups (360 ml) warm water, about 105°F
• 2 tablespoons light brown sugar
• 2 1/4 teaspoons active dry yeast
• 3 tablespoons (42 g) unsalted butter, melted and cooled slightly
• 4 to 4 1/2 cups (500 to 565 g) all-purpose flour, plus more as needed
• 2 teaspoons fine sea salt
• 2 tablespoons finely chopped fresh rosemary
• 1 teaspoon neutral oil, for the bowl
• 10 cups (2.4 L) water
• 2/3 cup (160 g) baking soda
• 1 large egg beaten with 1 tablespoon water
• 1 tablespoon coarse pretzel salt or flaky sea salt
• 1 teaspoon finely chopped fresh rosemary
• 2 tablespoons (28 g) unsalted butter
• 2 tablespoons all-purpose flour
• 1 cup (240 ml) whole milk, warmed
• 1 1/2 cups (170 g) freshly grated sharp cheddar cheese
• 1/4 teaspoon garlic powder
• Black pepper, to taste
• Salt, to taste