Pour the room temperature beer into a microwave safe bowl or large mug. Microwave for 45 seconds. It should be about 100 degrees.
Add the yeast to the beer, and stir until dissolved.
In a large mixing bowl, combine butter, sugar, salt, 3 c. flour, and the yeast-beer mixture.
Beat on medium speed until smooth.
Add enough flour to form a soft, smooth dough, but still sticky.
Turn the dough out onto a lightly floured surface, and knead for 5-6 minutes, or until it's very smooth and elastic.
Place in a large greased bowl, making sure to lightly grease the top of the dough, and cover it with plastic wrap.
Let it rise until double in size, about 1 hour.
Punch the dough down, and turn it out onto a lightly floured surface.
Divide the dough into 8 equal pieces.
Roll the pieces into 18-inch ropes, and form into pretzel shapes.
In a large pot, bring the water and baking soda to a boil.
Carefully drop the pretzels, one at a time, into the boiling water.
Boil for 1 minute, then remove from water with a slotted spoon, draining any excess water.
Place the pretzels 2 inches apart on greased baking sheets.
Brush the melted butter onto the pretzels, and sprinkle them with coarse sea salt.
Bake at 425 degrees for 10-11 minutes, or until golden brown.
Remove to wire racks to cool completely. Enjoy!!