In a large bowl, combine the 1 3/4 c. warm water, honey, and yeast. Let stand about 10 minutes or until yeast is dissolved and foamy. Using a wooden spoon, stir in the 4 eggs, melted butter, and salt. Gradually stir in as much of the flour as you can.

Turn dough out onto a lightly floured surface. Knead in enough of the remaining flour to make a moderately soft dough that is smooth and elastic (5 to 7 minutes total).

Shape dough into a ball. Place in a lightly greased bowl, turning once to grease surface. Cover and let rise in a warm place until double in size (1 to 1 1/2 hours).

Punch dough down. Turn out onto a lightly floured surface. Cover with a clean kitchen towel and let rest for 10 minutes.

To shape loaves, divide dough into 6 portions. Divide each portion into thirds (18 portions total). Gently roll 3 of the portions into 18-inch-long ropes (keep remaining portions lightly covered with plastic wrap). Place the 3 ropes 1 inch apart; braid. Repeat with another 3 portions of dough to make another braid. Place both braids side by side in a lightly greased 15x10x1-inch baking pan or baking sheet. Brush one side of a braid with water; lightly press braids together to make a double-braided loaf. Repeat with remaining dough portions to make 2 more double-braided loaves. Cover and let rise in warm place until nearly double in size (about 30 minutes).

Preheat oven to 350 degrees F. In a small bowl, combine the 1 egg and 1 tablespoon water; brush over loaves. Bake for 30 to 35 minutes or until loaves sound hollow when lightly tapped. Immediately remove loaves from baking pans. Cool on wire racks. Makes 3 double-braided loaves (16 servings each).