Preheat your oven to 350°F. While it heats, dice the zucchini into 1/4-inch pieces and finely chop the broccoli into pea-sized bits—keeping the vegetables small ensures they cook quickly and are the right texture for a baby to handle. Measure out the cheese, flour, and herbs so everything is ready to go.
Heat the oil in a small skillet over medium heat. Once warm, add the diced zucchini and chopped broccoli, stirring occasionally for 3-4 minutes until the vegetables are tender and slightly softened. This pre-cooking ensures the vegetables will be perfectly soft in the finished frittata rather than firm or raw.
In a small bowl, crack the eggs and whisk them together until well combined. Add the cheddar cheese, flour, oregano, and garlic powder, stirring until you have a smooth, homogeneous mixture. I like to make sure the flour is fully incorporated so there are no lumps—this creates a more delicate texture in the finished frittata.
Add the softened vegetables from Step 2 to the egg mixture from Step 3, folding gently until evenly distributed. Line a small baking dish (about 6x6 inches or similar) with parchment paper or lightly grease it, then pour the frittata mixture into the dish, spreading it out evenly.
Place the frittata in the preheated 350°F oven and bake for 15 minutes, until the eggs are set and the top is lightly golden. The frittata should be cooked through but still slightly moist—not dry or rubbery. A gentle touch in the center should show it's set but tender.
Remove the frittata from the oven and let it cool in the dish for a few minutes until it's safe to handle. Once cooled, turn it out onto a cutting board and cut into small, baby-friendly pieces—I typically cut them into 1-2 inch squares or strips that are easy for little fingers to grab and chew. Store any leftovers in an airtight container in the refrigerator.