Set an oven rack about 6 inches below the broiler and heat the broiler on high. Put a 10-inch oven-safe skillet on the stove so it is ready to use.

Warm the skillet over medium heat for about 1 minute. Add the olive oil and swirl it across the bottom.

Add the cherry tomatoes, the scallion whites, and 1/4 teaspoon of the salt to the skillet. Stir to coat everything in the oil.

Cook the tomatoes for 2 minutes over medium heat. Stir once or twice so the scallions soften and the tomatoes start to blister.

Keep cooking for 3 to 4 minutes more, pressing a few tomatoes with the back of a spoon as they soften. The tomatoes are ready when many of them have burst and released their juices.

Add the baby spinach to the skillet. Cook for 1 to 2 minutes, stirring gently, until the spinach wilts down.

Use a slotted spoon to transfer the tomato and spinach mixture to a bowl, leaving as much juice as you can in the skillet. Set the bowl near the stove.

Pour the water and milk into the same skillet. Raise the heat to medium-high and bring the liquid to a gentle simmer, with small bubbles around the edges.

Slowly whisk the quick grits into the simmering liquid. Keep whisking for about 30 seconds so the grits do not clump.

Lower the heat to low. Cook the grits for 5 to 7 minutes, stirring often with a spoon and scraping the bottom of the skillet, until the mixture is thick and creamy.

Turn off the heat. Stir in the shredded cheddar, the remaining 1/2 teaspoon salt, and the black pepper until the cheese melts completely.

Smooth the grits into an even layer in the skillet. Spoon the tomato and spinach mixture over the top, leaving a few open spots for the eggs.