Heat the oil in a large sauté pan over medium-high heat. Add the red onions and sprinkle with ½ tsp salt. Cook the onions until softened, about 3 to 4 minutes. Add the broccoli and sauté 2 to 3 minutes.
Add the chicken and cook until heated, another 2 to 3 mixtures. Remove from heat.
Fill the shortcrust pastry shell with the cooked chicken filling. Sprinkle the cheeses on top.
Mix the custard ingredients together until frothy, either by hand or using a hand mixer. Pour the custard over the filling as much as you can without overflowing.
Place the pan on a half sheet baking pan lined with a Silpat silicone mat or parchment paper to catch drips. Bake the quiche for 28 to 30 minutes or until the filling is mostly set (it will be slightly jiggly in the middle).
Allow the quiche to cool slightly, then remove from the pan and serve warm.
Feta cheese can be substituted for cotija cheese. The Mexican cheese blend consists of cheddar, Monterey Jack, and Queso Blanco. Use a pre-made blend or use your own preferred combinations.Trader Joes' Everything but the Elote seasoning blend is based on the seasonings made from Mexican street corn. It's made up of chile pepper, Parmesan cheese, chipotle powder, cumin, dried cilantro, sea salt, plus some cane sugar and corn flour. You can substitute a good chili powder or taco seasonings for this blend.If you're making the quiche ahead, allow to cool completely, then wrap in plastic wrap (still in the pan, if possible). It will keep for about a week in the refrigerator and up to a month in the freezer. If the quiche has been frozen, allow to defrost overnight in the refrigerator. When you're ready to serve, reheat in a 325°F oven for about 15 to 20 minutes or until heated through. Remove from the pan (if it hasn't been already) and serve warm.