Heat the oil in a large skillet over medium-high heat until it's shimmering and hot. Add the shrimp in a single layer and sear for two to three minutes per side, until they turn pink and opaque. Season with salt and pepper, then transfer to a plate.
In the same skillet, melt the butter and add the minced garlic. Sauté for about a minute, just until it turns fragrant and golden. This step is where a lot of the deep, savory flavor of the dish gets built, so don't rush past it.
Pour in the white wine and stir, scraping up any browned bits stuck to the pan. Add the heavy cream, Italian seasoning, and shredded cheddar. Stir constantly and let the sauce simmer gently over medium heat until it thickens to your liking.
Return the seared shrimp to the skillet along with any juices that collected on the plate. Toss everything together so each piece gets fully coated in that glossy, garlicky sauce.
Sprinkle freshly chopped parsley over the top for a pop of color and freshness. Serve the dish immediately while the sauce is still warm and silky, right from the skillet to the table.