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In a large bowl, stir yeast into water to soften.
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Add milk, oil, brown sugar, salt, oats, cinnamon, apples and walnuts. Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Add 2 cups flour and beat vigorously for 2 minutes.
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Gradually add remaining flour, a little at a time, until you have a dough stiff enough to knead.
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Turn dough out onto a floured surface.
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Knead, adding flour as necessary, until you have a smooth, elastic dough.
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Put the dough into an oiled bowl, turning once to coat the entire ball of dough with oil, and cover with a towel. Let rise in a warm place until puffy, about 1 hour.
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Grease two 9" x 5" or 10" x 5" loaf pans, and sprinkle with rolled oats.
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Turn dough out onto a lightly oiled work surface. Divide dough in half.
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Shape dough into loaves and place in prepared pans.
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Cover with a piece of lightly greased plastic and let rise until almost doubled, about 45 minutes.
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While the bread is rising, preheat the oven to 375°F. Just before baking, brush tops of loaves with egg/water mixture. Sprinkle with additional rolled oats.
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Bake for 30 minutes, or until internal temperature of loaves reaches 190°F. Immediately remove bread from pans and cool on a rack, to prevent crust from becoming soggy.
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Store, well-wrapped, for 5 days at room temperature, or freeze for up to 3 months.