Preheat oven to 350°F (180°C). Spray a 3-inch-tall 8-inch round cake pan with baking spray with flour. Line pan with parchment paper; spray parchment.

In the work bowl of a food processor, process chopped 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 1¼ cups (250 grams) 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. Spread batter into prepared pan.

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.

Meanwhile, in a small saucepan, heat orange juice and remaining 1⁄4 cup (50 grams) sugar over medium heat, whisking occasionally, until sugar dissolves, about 5 minutes.

Remove warm cake from pan, and place on a wire rack. Brush orange syrup onto cake. Let cool completely on wire rack. Garnish with orange slices, if desired. Store in an airtight container for up to 3 days.