In large bowl of stand mixer, combine 3 cups of the flour and the yeast.
Heat the wine, butter, sugar and salt over low heat until butter is not quite melted and temperature reaches 110°F. Stir this mixture into the flour/yeast mixture with paddle attachment. Add eggs and beat about 1 minute. I did not use the dough hook for this bread.
Remove paddle attachment. Scrape down sides and cover mixing bowl. Let rise in a warm place (80°F) for 1 hour.
I use my sink as a warm place for the bread to rise. I fill the sink half full of hot water, place a large colander in the water, and set the bowl with the bread in it on top of the colander. Cover all with a thick towel to hold in the heat.
Turn dough out onto well-floured surface. It will be very loose and sticky, not like regular bread dough. By hand, knead in the remaining cup of flour and all but 2 tablespoons of the grated cheese, until dough is smooth and elastic - about 5 minutes. Return to large bowl, cover, and let rise again for 1 hour.
Punch dough down and let rest 10 minutes. Shape dough into a long loaf and place on baking stone or lightly greased pan that has been dusted with cornmeal. Cover and let rest another 10 minutes. While dough is resting, turn oven to 350°F. After 10 minutes, pop loaf immediately into oven even if not completely preheated. Bake for 30-40 minutes until bread sounds hollow when tapped.
During last 5 minutes of baking, sprinkle remaining cheese on top of loaf.
Cool on rack; slice when completely cool for best results.
This bread slices well and tastes really great with butter. I did not notice much wine flavor (like I do with beer bread) but it might be worth trying with different types and flavors of wine. I'm going to try a red wine next.