Combine 2 cups flour, sugar, undissolved yeast, and salt in a large bowl. Heat milk, water, and oil until very warm (120° to 130°F); stir into flour mixture. Stir in enough remaining flour to make soft dough. Knead on floured surface until smooth and elastic, about 4 to 6 minutes. Cover; let rest on floured surface 10 minutes.
Divide into 14 equal pieces. Roll each piece to 20-inch rope. Cover; let rest 5 to 10 minutes until risen slightly. To shape into pretzels: Curve ends of each rope to make a circle; cross ends at top. Twist ends once and lay over bottom of circle. Place on 2 greased baking sheets.
Brush with beaten eggs. Bake at 350°F for 15 minutes. Remove from oven; brush again with eggs. Sprinkle with salt, cheese, poppy seed, or sesame seed.
Return to oven and bake for 15 minutes or until done. Remove pretzels from baking sheets; let cool on wire racks.