In a medium pot over high heat, add the milk and vegetable broth and bring to a boil.
3. Step
Whisk in the polenta and reduce the heat to low, whisking continuously for about 5 minutes, or until all the liquid has been absorbed and the polenta is creamy.
4. Step
Add the butter, salt, pepper, oregano, thyme, and rosemary and stir until well-combined.
5. Step
Transfer the polenta to the prepared baking sheet and spread out evenly with a spatula. Chill for at least 2 hours or up to 3 days to set.
6. Step
If baking, preheat the oven to 425ºF (220ºC).
7. Step
Make the aioli: Combine the mayonnaise, garlic, parsley, and lemon juice, salt, and pepper in a small bowl and mix until well-combined. Chill until ready to use.
8. Step
Carefully flip the baking sheet onto a cutting board to release the polenta. Slice in half lengthwise, and then cut into 22 equal-sized fries, each about 4 inches (10 cm) long and 1 inch (2 ½ cm) wide.
9. Step
If baking, use a spatula to transfer the fries onto wire racks set over 2 baking sheets. Brush each fry generously with olive oil. Bake for 30 minutes, flipping halfway through and brushing with more oil, until golden brown.
10. Step
If frying, heat the canola oil in a large pot until it reaches 375ºF (190ºC). Using a large spider, submerge 2 fries at a time into the oil and fry for 2-4 minutes, until golden brown and crispy. Remove from the oil and transfer to a plate lined with paper towels to cool for at least 5 minutes.
