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To make the dough: In a large mixing bowl, combine the flours, yeast, sugar, salt, and cardamom. In a small bowl, whisk together the water, egg, and oil and add to the dry ingredients. Mix for 2 minutes; the dough will begin to come together but be somewhat stiff. Add the chopped pear and mix to combine.
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Knead until the dough becomes more cohesive. Don't overwork the dough, or the pear will disintegrate and make the dough even wetter. Try folding the dough with a dough scraper until it becomes elastic, about 5 minutes. If the dough is very wet, add more flour 1 tablespoon at a time. Place the dough in a greased bowl, cover, and let rise for 45 minutes to an hour, until doubled.
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To make the filling: In a small bowl, combine the sugar, cinnamon, and flour.
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To assemble: Roll the dough to a 15" x 8" rectangle on a floured surface with the short side facing you. Spread the butter over the dough, leaving 1/2" of the far edge uncovered. Sprinkle the sugar mixture over the butter and roll up the dough, pinching the edge to seal. Place in a greased 9" x 5" loaf pan, seam side down.
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Cover and let rise for 40 to 45 minutes, until the loaf domes 1" above the rim of the pan. Toward the end of the rising time, preheat the oven to 375°F.
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Uncover the bread, slash the dough in four deep stripes across the top, and bake for 40 to 45 minutes. Tent the top of the loaf with foil after 30 minutes if needed. The bread is done when golden brown and the center reads 200°F when measured with a digital thermometer.
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Remove the loaf from the oven and cool it in the pan on a rack for 15 minutes. Tilt the bread out of the pan and return it to the rack to finish cooling completely before slicing.
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Storage information: Store the bread, tightly wrapped in plastic, at room temperature for several days; freeze for longer storage.