Preheat oven to 350 degrees. Butter 4 Ramekin and dust with Parmesan cheese. Sauté onion & broccoli in 3 tbs. extra virgin olive oil until onion cooked but not brown. Add garlic, sauté one minute. Add diced ham until warmed through.
Pour onion mixture equally into Ramekins. Top with shredded cheese. Whisk eggs, ½ cup milk, thyme, and salt/pepper to taste. Pour into Ramekins, carefully to avoid oven overflow.
Bake for approximately 30 minutes or until top is browned and center of top still has a little liquid to it.
Serve immediately garnished with herbs (Basil leaves, Rosemary, Sprig¿.etc.)