Melt the butter in a large skillet over medium heat.
When the butter has melted and has stopped foaming, add the diced potatoes, onion, bell pepper, and ham. Mix well.
Cook picadillo until nicely browned, stirring and turning frequently. Season with salt and freshly ground black pepper, to taste, and add the crumbled dried thyme.
Toast a slice of bread and put a fried egg on top. Serve everything together pouring some BBQ sauce on top.