How to Make It
In a large saucepan, melt the butter in the olive oil. Add the garlic and cook over moderate heat until fragrant, about 1 minute. Add the water, cream and milk and bring to a boil. Gradually whisk in the polenta until smooth. Cook over moderate heat, whisking often, until thickened, about 3 minutes. Stir in the cilantro, season with salt and pepper and let cool to warm, about 10 minutes.
Lay out three 12-by-12-inch pieces of foil on a work surface. Spoon the polenta in the center of the foil pieces in a long strip, leaving 2 inches at the edge. Bring the foil up and over the polenta and roll it into three 2-inch-wide logs. Refrigerate for about 1 hour, until firm.
Preheat the oven to 350°. In a small saucepan, heat the 2 tablespoons of olive oil. Add the garlic and cook over moderate heat until fragrant, about 1 minute. Scrape into a small bowl and let cool. Blend in the butter, cilantro, parsley and lemon juice and season with salt and pepper.
Unwrap the polenta logs and slice each one crosswise into 3/4-inch-thick rounds. In a large nonstick skillet, heat 1/8 inch of olive oil. Add one-third of the polenta rounds and cook over high heat, turning once, until browned, about 2 minutes per side. Transfer to a large rimmed baking sheet and repeat with the remaining polenta rounds. Reheat the rounds in the oven and transfer to plates. Dollop the polenta with the chimichurri butter and serve hot.