Preheat oven to 350 degrees F. Lightly oil and flour a 9-by-5-inch loaf pan.

Whisk all-purpose flour, whole-wheat flour, baking powder, baking soda, cinnamon, ginger, salt, allspice and cloves in a medium bowl until combined.

Beat squash puree, sugar, honey and oil in a large bowl with an electric mixer at medium speed until smooth, about 1 minute. Beat in egg and egg white. Turn off the mixer, add the dry ingredients and beat at low speed until combined. Scrape into the prepared loaf pan.

Bake the bread until lightly browned and a toothpick inserted into the center comes out clean, 45 to 50 minutes. Cool in the pan for 10 minutes, then turn out onto a wire rack and let cool for 30 minutes more. Serve warm.

Tip: To make your own squash puree, halve and seed one medium acorn or butternut squash. Place, cut-side down, on a lightly greased baking sheet. Bake in a preheated 375 degrees F oven until soft, about 50 minutes. Cool, then scrape out the flesh with a fork. Or simply use frozen (thawed) or canned squash puree. Find frozen squash puree near other vegetables in the freezer section and canned squash near the canned pumpkin.

MAKE AHEAD TIP: Tightly wrap in plastic wrap and freeze for up to 6 months. Unwrap and thaw on a wire rack at room temperature for 4 hours.