In an ovenproof skillet, heat the olive oil over medium heat.
1 tablespoon olive oil
Add the onion and cook, stirring often, until softened, about 5 minutes
¼ small yellow onion
Add the ham and spread into an even layer. Remove skillet from heat and set aside.
8 ounces smoked ham steaks
Add eggs, thyme, milk, salt, and pepper to a blender and blend until frothy about 30 seconds. You can also add these ingredients to a medium bowl and whisk briskly.
8 large eggs, ¼ cup milk, 2 teaspoons fresh thyme, salt and pepper
Add ½ cup of the cheese and blend on low until cheese is incorporated, about 10 seconds, or whisk into bowl with egg mixture if using that method.
1 cup Swiss cheese
Return skillet to medium heat and pour egg mixture over ham and onions. Cook without stirring for 5-8 minutes.
Place the skillet in the oven under broiler on high. Broil until eggs are mostly set, about 8 minutes.
Remove from oven and sprinkle remaining cheese over the top, and broil until cheese is melted, about 1-2 minutes. Remove from oven and allow to cool.
Toss arugula with oil, salt, and pepper. Lay over the top of warm frittata. Cut into wedges and serve warm.
arugula, olive oil, salt and pepper