Preheat the oven to 400°F. Lightly grease an 8x8-inch square baking pan with oil or vegan butter. Optional: Line the pan with parchment paper, leaving an overhang, and lightly grease the parchment for easier removal.
In a large bowl, combine the flour, cornmeal, sugar, salt, and baking powder.
Add the dairy-free milk and oil. Stir just until the batter is smooth and no dry pockets remain. Avoid overmixing so the cornbread stays tender.
Pour the batter into your prepared pan and spread evenly. Bake for 20 to 25 minutes, until the top is set and lightly golden, the edges pull slightly away from the pan, and a toothpick inserted in the center comes out clean or with a few moist crumbs.
Transfer the pan to a wire rack and let the cornbread cool in the pan for at least 15 minutes.
Slice into 12 squares and serve warm with vegan butter if desired.