Combine milk, vegetable broth , salt, pepper and cornmeal in a saucepan
Bring to a boil over high heat, stirring frequently until polenta thickens enough that it starts to spit.
Reduce heat, cover, and continue to cook for about 30 minutes. Stir frequently with a spoon or silicone spatula, scraping the bottom to prevent scorching. Polenta is ready when it becomes thick and pulls away from the sides of the pan but remains runny.
If polenta forms lumps, beat vigorously with a stiff whisk to remove.
If polenta becomes too firm or begins to set, add a small amount of water, stock, or milk and beat in with a whisk until liquid is fully incorporated and no lumps remain.
Turn the heat off. Add cheese and olive oil and stir with a whisk until smooth and creamy.
Serve right away.
Alternatively, you can spread it into an oiled baking sheet and let it firm up as it cools, then cut it into squares or circles. Refrigerate or freeze for later use. To reheat, place on the grill or saute in a tablespoon of olive oil for a few minutes