Mix the warm water, oil, honey, eggs and salt in a large mixing bowl. (Hint: measure the oil just before the honey, and the honey slips right out!).
Add about 2 or 3 cups of flour (I start here with 3 cups of bread flour), mix until good and messy. Add the yeast, mix well.
Continue adding cups of flour (this is where I switch to all-purpose) until thick enough to turn out and knead.
Turn out to a floured surface and knead for 10-15 minutes, adding flour as needed so dough doesn't stick. When dough is tacky but not sticky, and bounces back at you when you knead it, it is done.
Put a little oil in a big bowl, then coat the bowl before putting the dough in the bowl to rise. Flip the dough over in the oiled bowl to cover all sides of the dough with a film of oil. Cover with a lid or sheet of heavy plastic, let rise in a warm spot for 45 minutes.
Punch down, flip dough back onto floured surface. Divide in half or in thirds, form each piece into one loaf. Forms can be braided, coiled or woven and baked freestanding if dough was halved,. If using standard size (8-9 inch)loaf pans, make 3 loaves instead of 2.
Set freestanding loaves on pans lined with parchment paper or sprinkled with cornmeal. Let rise in a warm, but not hot, spot for 30-45 minutes, until doubled in size, covering with heavy plastic so dough doesn't dry out.
At this point preheat oven to 350F, and place rack at or just below center. Just prior to baking mix one egg with a few tablespoons of water, and use this to glaze your loaves. I use a standard baking brush. Brush lightly, so not to deflate the bread. Bake at 350F for 30 minutes.
When done, remove from pan and cool directly on a rack. Freezes beautifully.