1Stir yeast into 1 cup warm water in a large bowl; beat in flour, sugar, shortening, and salt to make a dough. Turn dough onto a floured surface and knead for 5 minutes.
2Place dough into a greased bowl and let rise in a warm place until doubled, about 1 hour. Punch down dough and divide into 12 equal-size pieces. Roll each piece into a rope 18 to 20 inches long.
3Preheat oven to 375 degrees F (190 degrees C). Grease a baking sheet.
4Shape each rope of dough into a pretzel on the prepared baking sheet; let pretzels rest for 5 minutes. Beat egg yolk with 1 tablespoon water in a small bowl and brush yolk mixture over each pretzel; sprinkle each with coarse salt.
5Bake in the preheated oven until pretzels are golden brown, about 15 minutes.
