In a large skillet, melt the butter over medium-high heat. Stir in the celery, frying pepper (or bell pepper), onion, garlic, chile, thyme and bay leaf; season with salt and pepper. Cover the pan and cook, stirring occasionally, until softened, 6 to 7 minutes.
Add the tomatoes and their juices and the sugar and bring to a bubble. Lower the heat, partially cover and cook for 15 minutes. Add the bread and lemon juice and stir to crumble the bread. Remove from the heat and let stand, covered, for 5 minutes. Discard the bay leaf.
In a large skillet, heat the EVOO (or vegetable oil), 1 turn of the pan, over medium-high heat. Add the ham steaks and cook, turning, until browned on the edges, 3 to 8 minutes.
To serve, place the ham steaks on plates. Top with the tomatoes, scallions and parsley. Pass the bread (or biscuits) and butter at the table.