Gently toss strawberries, 1 Tbsp. sugar, and a pinch of salt in a medium bowl. Let sit, stirring occasionally, until ready to use.
Grease a 13x9" pan with oil. Line with parchment paper, leaving an overhang on 2 long sides. Grease parchment with oil.
Whisk flour, cornmeal, baking powder, baking soda, 1 cup sugar, and 1 tsp. salt in a medium bowl.
Whisk eggs, egg yolks, greek yogurt, lemon zest, lemon juice, and vanilla in a large bowl until well combined.
Add dry ingredients to wet mixture and whisk gently to combine. Using a spatula, gradually fold in ¾ cup oil until batter is smooth and all of the oil is incorporated.
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.
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.
