Stir together 2 1/2 c of the flour, yeast, & salt in L bowl. Combine milk, water, 3 tbs olive oil, & honey in Med saucepan. Cook over med heat, stirring, until very warm (120 to 130 degrees). Stir liquid into flour mixture, then stir in 2 more cups flour.
Stir flour mixture until well combined and begins to leave side of bowl. Turn dough out onto a floured surface and work into a ball. Knead for 10 min., adding more flour as needed to keep from sticking.
Place dough in L greased bowl. Turn dough to coat evenly. Cover with plastic wrap or damp towel. Place bowl on lowest oven rack. Turn oven on to lowest setting for 1 min, then turn off. Let rise for 30 to 40 min or til doubled in size.
Punch down the dough. Knead on lightly floured surface 10 times to release air bubbles. Cover dough, let rest for 10 min.
To shape the dough: on a lightly floured surface, divide dough in half. Divide each half into thirds. Shape each third into into a 14 inch rope. Place three ropes side by side, on a greased L baking sheet. Braid ropes together, pinching ends to seal. Repeat with 2nd half of dough. Brush the loaves with beaten egg, then with olive oil. Cover loaves and let rise 20 min.
Meanwhile, preheat oven to 375. Bake loaves for 20 to 25 min until golden brown. Transfer loaves to wire rack to cool slightly.
Serve bread warm with butter or olive oil for dipping.