I like to prepare the polenta the day before and then fry them up while the sauce is simmering.
Line a small rimmed baking sheet with foil and grease with butter.
Bring the milk and broth to a simmer, stirring often to avoid scorching. Once bubble start to form around the edge of the pan, whisk in the polenta, salt and pepper.
Reduce heat to medium, whisking continuously until thick. About 5 minutes or so.
Pour polenta into the prepared pan, smooth with a spatula and let cool and firm up. If making this advance, stop at this point. Cover with plastic wrap and refrigerate.
When ready to serve, cut into squares or stamp out circles (may need to double the batch if using a biscuit cutter) with a biscuit cutter.
Heat a tablespoon of olive oil in a large non-stick skillet over medium heat. Once the oil is shimmering, place the polenta, smooth side down, into the oil of the pan. Cook 2 to 3 minutes, or until golden and crispy. Flip and repeat, then transfer to a paper towel lined plate and repeat with remaining polenta.
Simply Scratch Tip: This is something I have done the night before or the morning of, heck you could make this 2 days in advance if you wanted to. I really think time in the fridge not only helps to set the polenta but also cold polenta keeps together better when frying.