Heat the oven to 350 ° F. Grease a 9- by- 13- inch pan with cooking spray or softened butter. Line with a long piece of parchment paper that extends up and over the two long sides of the pan. Whisk together the oil, granulated sugar, and vanilla in a large bowl for 30 seconds. Whisk in the eggs, one at a time, and then the milk. Sprinkle the baking powder and salt into the bowl, one at a time, vigorously whisking after each. Gently fold in the flour with a flexible spatula just until the last streak disappears. The batter will be lumpy. Scrape the batter into the prepared pan and evenly scatter the strawberries on top. Generously sprinkle the cake with the turbinado sugar and bake for 55 to 60 minutes, rotating the cake at the halfway point. The cake is done when a wooden skewer inserted into the center comes out with a moist crumb or two. Remove from the oven and let cool to room temperature. Serve slices directly from the pan; or lift the cake from the pan with the parchment overhang, running a butter knife around the edges if it resists. Keep the cake, wrapped, on the counter for up to 3 days.