Preheat oven to 350°F (180°C). Spray an 8-cup cake pan* with baking spray with flour.

In the work bowl of a food processor, process oranges until almost completely puréed, about 30 seconds. (There should still be some small chunks remaining.)

In a medium bowl, whisk together flours, baking powder, and salt.

In the bowl of a stand mixer fitted with the whisk attachment, beat granulated sugar and eggs at medium-high speed until pale and thick, 5 to 7 minutes. With mixer on medium speed, add oil and vanilla, beating until combined. Add puréed orange, beating until completely combined. Add flour mixture, and beat at low speed just until combined, stopping to scrape sides of bowl. Pour batter into prepared pan. Tap pan on kitchen towel-lined surface 5 to 6 times.

Bake until top is golden and a wooden pick inserted in center comes out clean, about 1 hour and 15 minutes, loosely covering with foil after 45 minutes of baking to prevent excess browning. Let cool in pan for 10 minutes. Invert cake onto a wire rack, and let cool completely.

In a small bowl, whisk together confectioners’ sugar, orange zest and juice, and melted butter. Pour glaze over cooled cake. Serve immediately, or let stand until set, about 20 minutes. Store in an airtight container for up to 3 days.