Set a sheet pan on the top oven rack and preheat the oven to 425°. While oven is preheating, divide the baked beans into two oven-safe ramekins.
When the oven is preheated, remove the sheet pan. Spray with oil and arrange the bacon, sausage, mushrooms, and ramekins on the pan.
Return to the oven and bake at 425° for 10 minutes. While waiting, spread both sides of the bread with butter and slice in half.
Remove the pan from the oven and add buttered bread. Make 4 wells in the pan and crack an egg into each. Drop cherry tomato halves in any empty spaces.
Return to the oven and cook an additional 5 minutes for over-easy eggs, 7 minutes for over-medium, or 9 minutes for over-hard.
Sprinkle the pan with fresh thyme, salt, and pepper. Serve hot with HP sauce.