Start by preheating your oven to 375°F so it's ready when you need it. While the oven heats, thinly slice the red onion and heat the olive oil in a skillet over medium heat. Add the onions and cook for 8-10 minutes, stirring occasionally, until they're soft and lightly caramelized—this develops sweetness that balances the savory cheese and eggs. While the onions cook, cut your sourdough bread into 3/4-inch cubes and measure out your cheeses (I always use freshly shredded mozzarella when I can, as pre-shredded versions contain anti-caking agents that prevent smooth melting). Finely chop your fresh parsley and set aside for garnish.

In a large bowl, whisk together the room-temperature eggs and whole milk until well combined—room temperature eggs incorporate more smoothly into the milk and create a more uniform custard. Add the dried thyme, salt, and black pepper to taste. Whisk again until the mixture is homogeneous and the seasonings are evenly distributed. The custard should be smooth and pale yellow. Set this mixture aside until you're ready to assemble the strata.

Lightly grease a baking dish (a 9x13-inch dish works well) with butter or oil. Begin layering by spreading half of the bread cubes on the bottom of the dish, then distribute half of the caramelized onions from Step 1 over the bread. Sprinkle half of the combined cheddar and mozzarella cheese over the onions. Pour about half of the egg custard mixture from Step 2 evenly over this first layer, letting it soak into the bread. Repeat the layers: remaining bread, remaining onions, remaining cheese, and finally the remaining egg custard. I like to let the assembled strata sit for 15-20 minutes before baking so the bread fully absorbs the custard and the flavors meld together—this creates a more cohesive, custardy texture throughout.

Transfer the assembled strata to your preheated 375°F oven and bake for 50-60 minutes until the top is golden brown and a knife inserted in the center comes out clean or with just a few moist crumbs (it should not be runny). The strata will puff up slightly as it bakes from the eggs cooking and steam forming. If the top begins browning too quickly, loosely tent it with aluminum foil for the final 15-20 minutes of baking.

Remove the strata from the oven and let it rest for 5-10 minutes before cutting. This allows the custard to set completely and makes slicing cleaner. Top each serving with a generous sprinkle of the fresh parsley from Step 1 for color and a bright herbal note that cuts through the richness of the cheese and eggs.