1. In a large bowl mix 2 cups flour, cornmeal, salt, baking soda, and dry yeast. Add the butter.
2. Gradually add the hot water and honey and beat for 2 minutes at medium speed with an electric mixer. Add 1/2 cup more flour and beat for 2 minutes longer.
3. Stir in rice and enough extra flour to make a stiff dough. Turn out onto a lightly floured board and knead for 10 minutes, or until smooth and satiny. Put in an oiled bowl and turn to oil the top. Cover and let rise in a warm place until doubled in volume, about 1 hour.
4. Punch the dough down and turn onto floured board. Halve dough, cover, and let rest for 10 minutes. Roll each half into a 9-inch round. Put on an oiled baking sheet. Cover and let rise in a warm place until doubled in bulk, about 1 & 1/4 hours.
5. Preheat the oven to 375 degrees.
6. Using the handle of a wooden spoon, make deep indentations in the rounds at 1-inch intervals. Brush loaves with beaten egg. Bake for 35 minutes, or until the loaves sound hollow when tapped on the bottom. Cool on wire racks.