Measure out the water into a medium mixing bowl. Sprinkle the yeast onto the water, and stir it to dissolve.
Add the sugar, brown sugar, salt and stir to dissolve.
When blended, add the flour, and mix until dough is formed.
Knead the dough until smooth and elastic. Then, leaving the dough in the mixing bowl, cover and allow rising for at least 1/2 hour.
While dough is rising, prepare a baking soda water bath by combining 2 cups warm water and 2 tablespoons baking soda. Stir the mixture often until ready to use.
After dough has risen, pinch off small bits of dough and roll each into a long rope (about 1/2 inch or less thick) and shape into pretzel shape.
Dip each pretzel carefully into the soda solution and then place onto a greased baking sheet. When all the pretzels have been laid out, cover, and allow them to rise again.
Bake in oven at 450 for about 10 minutes or until golden. Immediately after removing form the oven, brush with melted butter and sprinkle with coarse salt. Serves 4 to 6.