Preheat oven to 350°F. Gently crush the dehydrated strawberries in the bag and set aside.
Grease a 9x13" pan with cooking spray or oil. Line with parchment paper, leaving an overhang on both long sides. Grease parchment with oil. Sprinkle with 2-3 tablespoons of sugar, tilting pan to coat in an even layer (I used a baking stone pan as pictured, so I did not use the parchment paper).
Whisk flour, 1 cup sugar, cornmeal, salt, baking powder, baking soda in a medium bowl. Whisk eggs, egg yolks, sour cream, zest from both lemons, 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 oil until batter is smooth and oil is incorporated (or use a mixer with paddle). Fold in the crushed, dehydrated strawberries.
Scrape batter into prepared pan and spread evenly. Arrange sliced, fresh strawberries on top of batter to cover. Sprinkle all over with remaining 2 tablespoons sugar.
Bake cake until risen and deeply golden, 45-50 minutes. Check that tester inserted in center comes out clean, no damp spots. Dust with some powdered sugar if you like, this is optional. Let cool before slicing.