Preheat the oven to 425°F with a rack in the center position.
Place the bacon in a medium ovenproof skillet. Set the skillet over medium heat and cook, stirring occasionally, until the bacon crisps and the fat is rendered, 5 to 7 minutes. Using a slotted spoon, transfer the bacon to a paper towel–lined plate, reserving the fat in the pan.
Add the onion to the bacon fat and cook, using a wooden spoon to scrape any browned bits from the bottom, until softened and translucent, about 5 minutes. Add the garlic and half of the chard and cook, stirring occasionally, until the chard is wilted, then add the remaining chard to wilt, about 2 minutes total. Return the crispy bacon to the pan and add half the olives. Remove the skillet from the heat.
Using a spoon, create four wells in the chard mixture. Crack one egg into each well, one at a time. Pour the cream over the entire dish. Bake until the egg whites are no longer transparent, 10 to 12 minutes.
Meanwhile, melt the butter in a small skillet over medium heat. Add the panko and cook, stirring to coat, until toasted, about 2 minutes.
Sprinkle the toasted panko all over the baked eggs. Add the feta, the remaining olives, the chives, pepper, and flaky salt. Serve with crusty bread alongside.