In a large mixer bowl, combine 1 cup flour, yeast, sugar and salt; mix well. In saucepan, heat 1 cup water and butter until warm (120 - 130 °F; butter does not need to melt). Add to flour mixture. Blend at low speed until moistened; beat 2 minutes at medium speed. Add 1/2 cup flour. Beat 2 minutes at high speed. By hand, gradually stir in enough remaining flour to make a soft dough. Knead on floured surface until smooth and elastic, 5 to 8 minutes. Place in greased bowl, turning to grease top. Cover; let rise in warm place until double, about 40 to 60 minutes.
Punch down dough. Divide into 12 equal pieces. On lightly floured surface, roll each into a 20-inch rope. Shape into pretzels. Place on greased baking sheets. Cover; let rise in warm place, about 5 to 15 minutes. Mix egg yolk and 1 tablespoon water; brush on pretzels. Sprinkle with coarse salt. Bake at 375 °F. for 15 to 20 minutes or until done. Cool on racks.