Dissolve yeast and 1 teaspoon sugar in warm water in a large bowl, stirring well. Let stand 5 minutes or until bubbly. Add remaining sugar, shortening, 1 egg, 1 teaspoon salt, and 3 1/2 cups flour; beat at low speed of electric mixer until smooth. Stir in enough remaining flour to make a soft dough.
Place dough in a greased bowl, turning to grease top. Cover and let rise 1 hour or until doubled in bulk. Punch dough down, and let rest 5 minutes.
Turn dough out onto a lightly floured surface, and knead 4 to 5 times. Divide dough into 4 equal portions. Divide each portion into 10 pieces. Roll each piece into an 8-inch rope, and place on greased baking sheets. Brush top of breadsticks with beaten egg. Sprinkle with remaining salt and caraway seeds.
Cover and repeat rising procedure 50 minutes or until doubled in bulk. Bake at 425° for 10 minutes or until golden brown. Place on wire racks to cool.
Parmesan Salt Sticks: Substitute 1/4 cup grated Parmesan cheese for the caraway seeds. Continue with recipe as directed.
Garlic Salt Sticks: Substitute 2 1/2 tablespoons garlic salt for the caraway seeds and 2 remaining tablespoons salt. Continue with recipe as directed.