In a large bowl, combine 2 cups flour, sugar, yeast, salt and caraway seeds. In a small saucepan, heat the milk, beer and oil to 120°-130°; add to dry ingredients. Beat just until moistened. Stir in enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 4-6 minutes. Cover and let rest for 10 minutes. Divide dough into 14 equal portions; roll each into a 20-in. rope. Cover and let rest 10 minutes longer.
Twist into pretzel shapes. Place on greased baking sheets; brush with eggs. Bake at 350° for 15 minutes.
Brush again with eggs; sprinkle with Gouda and coarse salt. Bake 12-15 minutes longer or until golden brown. Remove to wire racks. Serve warm.