Measure 1 cup of the bread flour, all the rye flour, and the yeast, caraway seeds, and salt into large bowl of electric mixer.
In saucepan, heat beer, oil, and molasses to 120°F – 130°F Pour liquids over dry ingredients in bowl and beat on high speed until smooth, about 3 minutes, clean down bowl with rubber spatula. Add remaining bread flour and stir until flour is evenly blended into mixture.
Turn batter into greased 1 1/2 quart casserole dish. Let rise in warm place until almost doubled, about 45 minutes.
Heat oven to 350°F Bake until wooden skewer inserted in the center comes out clean, about 30 minutes. Cool 10 minutes, then remove bread from baking dish and cool on wire rack.