Preheat the oven to 315 degrees F. Spray 6 cups of a muffin tin lightly with nonstick cooking spray.
Heat the olive oil over high heat in a saute pan until it begins to smoke slightly. Add the broccoli and caramelize; season with salt and freshly cracked pepper. After about 3 minutes, add the shallots and quickly saute. Cool completely on a tray lined with a paper napkin.
Combine the cream, whole eggs and yolk in a bowl and whisk in the marjoram and nutmeg. Season with salt and freshly cracked pepper.
Add 2 tablespoon of the vegetable filling to each muffin cup. Sprinkle on a layer of goat cheese and grated Swiss. Divide the egg custard mixture evenly among the muffin cups. Top with any leftover vegetables and cheese.
Bake until an inserted skewer comes out clean, with no wet custard clinging to it, about 25 minutes. If necessary, bake in additional 5-minute increments. The tops should be golden brown.