Grease a 1-quart casserole or an 8x 1 1/2-inch round baking pan; set aside. In a large bowl stir together 1 cup of the all-purpose flour, the sugar, yeast, the 2 teaspoons caraway seeds, the salt, and dill. Add the the 3/4 cup warm water, the egg, and butter.
Beat with an electric mixer on low to medium speed for 30 seconds, scraping side of bowl constantly. Beat on high speed for 3 minutes. Using a wooden spoon, stir in the rye flour and the remaining all-purpose flour (batter will be stiff).
Spoon batter into the prepared casserole, spreading to edge. Cover and let rise in a warm place until double in size (50 to 60 minutes). If desired, lightly brush top of loaf with additional water and sprinkle with additional caraway seeds.
Preheat oven to 375°F. Bake about 25 minutes or until bread is golden brown and sounds hollow when lightly tapped. Immediately remove bread from pan. Cool on a wire rack.