In a small bowl, combine 1 cup (240 grams) warm water, sugar, and yeast. Let stand until foamy, about 5 minutes.

In the bowl of a stand mixer fitted with the paddle attachment, combine flours, honey, 1 egg (50 grams), butter, and salt. Add yeast mixture, and beat at low speed until combined and a shaggy dough forms.

Switch to the dough hook attachment. Beat at medium-low speed until dough pulls away from sides of bowl, 5 to 8 minutes. (Dough will be soft and slightly sticky.)

Oil a large bowl. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 45 minutes to 1 hour.

Lightly dust work surface with all-purpose flour. Punch down dough, and turn out onto prepared surface. Cover and let stand for 20 minutes. Pat dough into a 9x7-inch rectangle, with one short side closest to you. Fold bottom third of dough up; starting at short side where dough is folded, roll up dough into a log. Pull log, seam side down, toward you to create tension on surface.

Lightly spray a 9x5-inch loaf pan with baking spray with flour. Place dough, seam side down, in prepared pan, tucking ends slightly. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size and risen just above sides of pan, about 1½ hours.

Preheat oven to 375°F (190°C).

In another small bowl, whisk together 1 tablespoon (15 grams) water and remaining 1 egg (50 grams). Using a pastry brush, brush egg wash onto dough; sprinkle with oats.

Bake until golden brown and an instant-read thermometer inserted in center registers at least 190°F (88°C), about 30 minutes. Let cool in pan for 15 minutes. Remove from pan, and let cool completely on a wire rack. Store in an airtight container for up to 5 days. Tightly wrap in plastic wrap, and freeze for up to 3 months.