In a medium bowl, whisk together the eggs, half-and-half, a few dashes of nutmeg and some salt and freshly ground black pepper. Pour half of the egg mixture over everything in the pan.
Add the rest of the bread, pressing down slightly, the remaining cheese and bacon to the pan. Pour the rest of the egg mixture over the top and sprinkle the Parmigiano Reggiano over everything.
Transfer the cake pan to the oven and bake until puffy and golden brown on top, about 20 minutes. It shouldn't look wobbly in the middle. (Don't worry if the puffiness falls down when you take it out of the oven, that'll happen).
Once the cake has been baking for about 10 minutes, place a medium-size saucepot over medium-low heat with the peach halves and their juices. Sprinkle the brown sugar, cinnamon and a few more dashes of nutmeg over the top. Bring everything up to a bubble, stirring occasionally, then remove from the heat and stir in the fresh berries. Set the sauce aside until everything is ready.
While the sauce is heating up, place the skillet you cooked the bacon in back over medium-high heat with 1 turn of the pan of EVOO, about 1 tablespoon. Add the ham steak and cook until golden brown and heated through, 3-4 minutes per side. Remove from pan and cut it into 4 pieces.
Once everything is ready, serve a wedge of the egg cake with a ham steak and a generous ladle of the peach-berry sauce alongside.