Preheat your oven to 375°F while you get the topping ready. In a bowl, toss the tomatoes, diced ham, minced garlic, fresh thyme, and olive oil until everything is coated. Spread the mixture into a tight circle on a small baking sheet so the juices pool together instead of spreading thin.
Slide the baking sheet into the oven and roast for about 15 minutes, until the tomatoes start to soften and burst. You'll notice the juices mingling with the ham and garlic to form a light, savory sauce right on the pan. Once it looks glossy and slightly collapsed, pull it out and set it aside.
While the tomatoes roast, place a small skillet over medium to medium-high heat and let it sit empty for a full minute. This dry preheat is the secret to that crispy frizzled edge. Add one tablespoon of neutral oil per egg and let it heat until it just starts to shimmer.
Crack one egg directly into the hot oil and stand back a little, since it will bubble and sizzle right away. Season with a touch of salt and pepper as the white starts to set. Tilt the pan slightly and spoon hot oil over the top of the egg to help the whites finish cooking evenly.
Once the bottom is deeply golden and crisp and the white is fully set, remove the pan from the heat and count to ten before touching the egg. This short rest keeps the egg from tearing. Slide your fish spatula underneath and gently lift it onto a plate.
Ladle about half a cup of warm garlic cheese grits onto each plate as your base. Spoon the roasted tomato and ham mixture over the grits, making sure to include some of that flavorful pan sauce. Top each plate with one frizzled egg and serve right away while everything is hot.