In a large bowl, dissolve sugar into hot water. Sprinkle yeast over top and let stand for 5 minutes or until frothy.
Whisk in butter and salt. Stir in 3 1/2 cups (875 mL) of the flour until a ragged dough forms.
Turn dough out onto floured work surface and knead until smooth, adding more flour if sticky.
Place dough in a greased bowl; cover and let stand to rise for about 1 hour or until doubled in size.
Meanwhile bring water and baking soda to boil. Reduce heat to a simmer.
Cut dough equally into 32 portions. Roll each into a 6 inch (15 cm) log. Add about 4 at a time into water for about 30 seconds.
Using a slotted spoon remove to a parchment or silicone lined baking sheet. Place 16 sticks on 1 baking sheet. Repeat with remaining sticks and another prepared baking sheet.
In a small bowl, whisk together egg yolk and water. Brush over top of pretzel sticks. Sprinkle with coarse salt. Bake 1 sheet at a time in centre of a 425oF (220oC) oven for about 10 minutes or until deep golden brown.
In a saucepan, melt butter over medium heat. Stir in flour and cook for 1 minute.
Gradually whisk in milk. Cook, whisking gently for about 6 minutes or until starting to bubble and thicken. Reduce heat to low; stir in cheese until melted. Stir in salt and pepper.
Stir in 1 small clove garlic, rasped when adding milk to the sauce.
Buffalo Cheese Variation:
For a kick to the sauce stir in 2 tbsp (30 mL) buffalo hot sauce into the sauce after cheese is melted.
Cover and refrigerate sauce up to 3 days. Warm over low heat in a saucepan, stirring occasionally or in microwave in 30 second intervals until warm.