Begin by cooking the frozen artichoke hearts according to the package instructions. Once cooked, drain the artichokes thoroughly and set them aside to cool slightly. When they are cool enough to handle, coarsely chop the artichokes and set them aside.
Preheat your oven to 350°F and position a rack in the middle of the oven.
In a large skillet, melt the butter and olive oil together over medium-high heat. Add the finely chopped onion to the skillet and cook, stirring frequently, until the onion becomes tender and translucent, about 5-7 minutes. Add the minced garlic to the skillet and continue to cook for an additional minute until fragrant. Stir in the dried oregano and the chopped artichokes, then remove the skillet from the heat.
Grease an 11x7-inch baking dish with butter or cooking spray. Sprinkle 1/4 cup of the shredded Monterey Jack cheese evenly over the bottom of the greased baking dish. Top the cheese with the artichoke and onion mixture, spreading it out evenly.
In a large mixing bowl, whisk together the eggs, milk, salt, white pepper, and ground nutmeg until well combined and slightly frothy. Stir in the shredded Monterey Jack cheese and another 1/4 cup of the cheese until evenly distributed.
Pour the egg mixture over the artichoke and onion mixture into the baking dish, ensuring that it is evenly distributed.
Place the baking dish in the preheated oven and bake, uncovered, for 30 minutes. After 30 minutes, remove the dish from the oven and sprinkle the remaining 1/4 cup of Monterey Jack cheese over the top of the frittata. Return the dish to the oven and continue baking for an additional 6-8 minutes, or until a knife inserted into the center of the frittata comes out clean.
Remove the frittata from the oven and let it cool for a few minutes before slicing and serving. If desired, garnish with minced fresh chives before serving.