In a medium saucepan, bring the water to a gentle boil over medium heat. Add the grated garlic, dried oregano, salt, and black pepper.
Slowly whisk in the polenta to prevent lumps. Reduce heat to low and cook, stirring constantly, until thick and smooth, about 8–10 minutes.
Remove from heat and stir in the Parmesan cheese, and butter, until fully melted and well combined.
Lightly grease an 8×8-inch baking dish with 1 tablespoon olive oil. Pour the hot polenta into the pan and spread evenly using a spatula, smoothing the top.
Cover and refrigerate for at least 1–2 hours, or until completely firm. I sometimes leave overnight.
Once chilled, remove the polenta from the pan and place on a cutting board. Slice into 4-inch-long fry shapes, about ½-inch thick.
Preheat oven to 425°F (220°C) and line a baking sheet with parchment paper.
Arrange the polenta fries in a single layer on the baking sheet. Lightly brush or spray the fries with the remaining 1 tablespoon olive oil.
Bake for 25–30 minutes, flipping halfway through, until golden brown and crisp on the outside.
Remove from oven, add grated parmesan and garnish with parsley if desired. Serve warm.