Stewed Tomato Shirred Eggs

2 tablespoons salted butter
1 yellow onion, finely chopped
1 teaspoon salt
8 cups diced fresh tomatoes, with juice
1/4 cup packed fresh basil leaves, chopped
2 tablespoons light brown sugar
1 tablespoon red wine vinegar
4 garlic cloves, minced
1/4 teaspoon crushed red pepper
1/2 cup soft, fresh breadcrumbs
8 thin country ham or prosciutto slices
6 large eggs
1/2 teaspoon salt
1/2 teaspoon black pepper
Fresh basil, flat-leaf parsley, or chervil leaves Crusty bread (optional)

Prepare the Stewed Tomatoes:
Melt butter in a 3-6 quart heavy saucepan or Dutch oven over medium.
Add chopped onion and salt; cook, stirring occasionally, until slightly caramelized, about 10 minutes.
Stir in tomatoes, chopped basil, brown sugar, vinegar, garlic, and crushed red pepper.
Cover and increase heat to medium-high; bring to a boil.
Reduce heat to medium-low, and simmer 30 minutes.
Uncover and cook 10 minutes.
Stir in breadcrumbs, and cook until tomato mixture is slightly thickened, about 5 minutes.
Proceed with recipe as directed, or chill overnight in an airtight container.
Stewed Tomatoes are best the next day.
If chilling overnight, bring to a simmer before proceeding with recipe.
Preheat oven to 350°F.
Place ham slices in a single layer on a parchment paper-lined baking sheet;
top with a second piece of parchment paper.
Place a second baking sheet on top of parchment to weigh it down.
Bake on middle rack in preheated oven until ham is crisp and brown, 12 to 15 minutes.
Cool to room temperature.
Remove and discard parchment.
Spoon simmering Stewed Tomatoes into a greased large shallow baking dish or ovenproof 12-inch skillet.
Using the back of a spoon, press 6 evenly spaced indentations in Stewed Tomatoes.
Crack eggs, and slide 1 egg into each indentation.
Sprinkle eggs evenly with salt and black pepper.
Bake at 350°F on middle rack until whites are a little jiggly and yolks are barely set, 12 to 15 minutes.
Divide eggs and Stewed Tomatoes evenly among 4 bowls.
Top evenly with herbs. Stand ham chips upright in bowls.
Serve with crusty bread, if desired.