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1
In a large bowl, stir the brown sugar into 2 cups of warm water until dissolved.
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2
Sprinkle the yeast over the water and let stand until foamy, about 5 minutes.
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3
Stir in the vegetable oil and 3 cups of the flour.
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4
Knead in the remaining 2 3/4 cups of flour; the dough will be slightly sticky.
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5
Transfer the dough to a floured work surface and knead until silky, about 3 minutes; if the dough is very sticky, knead in up to 1/4 cup more flour.
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6
Transfer the dough to an large, oiled bowl, cover with plastic wrap and let stand at room temperature until doubled in bulk, about 45 minutes.
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7
Preheat the oven to 450.
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8
Line 3 large cookie sheets with parchment paper and butter the paper.
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9
Punch down the dough and turn it out onto a floured work surface.
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10
Knead the dough lightly, flatten it out and cut it into 24 pieces.
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11
Roll each piece into a 9-inch stick about 1/2 inch thick.
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12
Transfer the sticks to the prepared cookie sheets, leaving at least 2 inches between them.
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13
Let stand uncovered until puffed, about 25 minutes.
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14
In a large, deep skillet, stir the baking soda into 2 quarts of water and bring to a simmer over high heat.
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15
Reduce the heat to moderate.
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16
Using 2 slotted spoons, carefully transfer 6 pretzel sticks at a time to the simmering water 30 seconds, turning once; add about 1 cup of hot water after before cooking the second batch of pretzels.
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17
Transfer the pretzel sticks to paper towels to drain, then return them to the cookie sheets, spacing them evenly.
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18
Brush the pretzel sticks with the egg wash and sprinkle with salt.
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19
Bake until richly browned, about 10 minutes.
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20
Serve warm or at room temperature, with mustard.
