Cheesy Grits with Fried Eggs and Bacon

Name: Cheesy Grits with Fried Eggs and Bacon
Ingredients: 3 cups water; 3/4 cup stone-ground corn grits, such as Anson Mills, Logan Turnpike Mill, or Palmetto Farms; 1 teaspoon kosher salt, plus more for serving; 1/2 cup grated Parmesan or sharp cheddar cheese (optional); 1 medium avocado; 4 strips bacon (not thick-cut, about 5 ounces); 1 cup cherry or grape tomatoes (about 5 ounces); 3 tablespoons unsalted butter, divided; 1/4 cup whole or 2% milk; 4 large eggs, divided; Freshly ground black pepper, for serving