Preheat your oven to 375°F and spray a 9x13-inch baking dish with cooking spray. While the oven heats, prepare all your vegetables: cut the broccoli into 1-inch florets, dice the red bell pepper into 1/2-inch pieces, and dice the yellow onion into 1/2-inch pieces. Having everything prepped and ready makes the cooking process smooth and ensures the vegetables cook evenly in the next step.
Heat the olive oil in a large skillet over medium-high heat. Once shimmering, add the diced bell pepper and onion, cooking for about 4 minutes until they begin to soften and the onion becomes slightly translucent. Add the broccoli florets and 2-3 tablespoons of water, then cover the skillet and cook for 1 minute to steam the broccoli slightly. Uncover and cook for 1 minute more, stirring occasionally—this brief cooking ensures the vegetables are tender-crisp but not mushy, and they'll continue to cook gently in the oven. I like to taste a piece of broccoli at this point to make sure it has a bit of bite left to it.
In a large bowl, whisk together the room-temperature eggs, low-fat milk, kosher salt, and ground black pepper until well combined and slightly frothy. The room-temperature eggs are important because they incorporate more smoothly and create a more even texture throughout the casserole. Stir in 1/2 cup of the shredded sharp Cheddar cheese until evenly distributed throughout the mixture.
Spread the sautéed vegetables from Step 2 evenly in the prepared 9x13-inch baking dish. Pour the egg custard mixture from Step 3 over the vegetables, making sure they're distributed evenly. Sprinkle the remaining 1/2 cup of shredded Cheddar cheese over the top. Bake in the preheated 375°F oven for 30 to 35 minutes, until the eggs are set but still slightly soft in the very center—they should jiggle just barely when you gently shake the dish. I find the casserole is perfectly done when the edges are firmly set but there's still a little give in the middle, as carryover cooking continues while it cools.
Remove the casserole from the oven and let it rest at room temperature for about 10 minutes. This cooling period allows the eggs to continue setting and makes the casserole easier to cut into neat portions. Just before serving, top with the pico de gallo or fresh salsa, distributing it evenly across the top for a fresh, vibrant finish.