In the bowl of a stand mixer fitted with the paddle attachment, whisk together flour, oats, sugar, salt, yeast, cinnamon, nutmeg, allspice, and cloves by hand.
In a small bowl, whisk together warm apple cider and melted butter. Add cider mixture to flour mixture, and beat at medium speed until combined, about 30 seconds. Switch to the dough hook attachment. Beat at low speed until dough is smooth and elastic, about 5 minutes. Add apple, and beat until most of apple pieces are picked up by dough, about 1 minute.
Turn out dough onto a lightly floured surface, and knead gently to completely incorporate apple, about 5 times. Lightly oil a large bowl. Shape dough into a smooth ball, and place in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, about 1 hour.
Spray a 9x5-inch loaf pan with cooking spray.
Lightly pat dough into a 9-inch circle. Fold top third of dough to center, pressing to seal. Fold bottom third over folded portion, pressing to seal. Fold dough in half lengthwise so long edges meet. Using the heel of your hand, firmly press edges to seal. Place dough, seam side down, in prepared pan. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 30 to 45 minutes.
Preheat oven to 350°F (180°C).
Make Oat Streusel: In a small bowl, stir together flour, oats, sugar, cinnamon, salt, and nutmeg. Add melted butter, and stir until mixture is crumbly.
Make egg wash: In a small bowl, whisk together egg and 1 tablespoon (15g) water. Brush top of loaf with egg wash, and sprinkle with Oat Streusel.
Bake until an instant-read thermometer inserted in center registers 205°F (96°C), 50 to 55 minutes. Let cool in pan for 15 minutes. Remove from pan, and let cool completely on a wire rack. Serve with softened butter or apple butter.