Step 1

Preheat oven to 350°. Gently toss strawberries, 1 Tbsp. sugar, and a pinch of salt in a medium bowl. Let sit, stirring occasionally, until ready to use.

Step 2

Grease a 13x9" pan with oil. Line with parchment paper, leaving an overhang on 2 long sides. Grease parchment with oil. Generously sprinkle pan and parchment with sugar, tilting to coat pan in an even layer; tap out excess.

Step 3

Whisk flour, cornmeal, baking powder, baking soda, 1 cup sugar, and 1 tsp. salt in a medium bowl. Whisk eggs, egg yolks, sour cream, lemon zest, lemon juice, and vanilla in a large bowl until well combined. Add dry ingredients to sour cream mixture and whisk gently to combine. Using a spatula, gradually fold in ¾ cup oil until batter is smooth and homogenous with all of the oil incorporated.

Step 4

Scrape batter into prepared pan and spread evenly. Using a small spoon, dollop jam onto surface. Using a butter knife or small offset spatula, gently swirl jam into batter. Arrange reserved strawberries on top of batter in even rows, touching at widest points. Sprinkle all over with remaining 2 Tbsp. sugar.

Step 5

Bake cake until risen and deeply bronzed with no damp spots in the middle and a tester inserted into the center comes out clean, 40–45 minutes.

Step 6

Do Ahead: Cake can be made 4 days ahead. Cover with foil and store at room temperature.