Preheat oven to 350°F (180°C). Spray an 8-inch square baking pan with baking spray with flour. Line bottom of pan with parchment paper.

In the bowl of a stand mixer fitted with the whisk attachment, beat sugar, lemon zest, and thyme at low speed until fragrant, 1 to 2 minutes. Add eggs, and beat at medium-high speed until mixture is thick and pale, 5 to 7 minutes. With mixer on medium-low speed, gradually add oil and vanilla, beating until combined. Add yogurt, beating until combined.

In a medium bowl, whisk together flour, baking powder, and salt. With mixer on low speed, gradually add flour mixture to sugar mixture, beating until just combined and stopping to scrape bottom and sides of bowl. Spread batter into prepared pan.

Bake until a wooden pick inserted in center comes out clean, 30 to 35 minutes. Let cool in pan for 5 minutes. Remove from pan, and let cool completely on a wire rack. Brush with oil just before serving. Garnish with lemon, if desired. Store in airtight container for up to 3 days.