Adjust rack to center position of oven. Preheat oven to 400°F. Generously grease a 12-cup muffin pan with softened butter or spray with non-stick cooking spray.
In a large bowl, whisk together eggs, milk, salt, and pepper until well-combined. Pour thawed hash browns into a large colander or sieve and press down with the back of spoon to squeeze out all of the water; add the drained potatoes to the egg mixture along with the bacon, cheddar, and jalapeño (if using). Stir well.
Evenly divide the egg mixture between the 12 greased muffin cups, ensuring that there is an equal amount of filling-to-egg ratio in each cup. Sprinkle a teaspoon of grated Parmesan on top of each muffin (if using).
Bake for 20 to 25 minutes or until the muffins are puffy and light golden brown. Remove pan to a wire rack and run a thin knife or spatula around each mini frittata to loosen. Allow to cool for 5 minutes, then run knife around the edges again and carefully remove frittatas from pan. Serve warm or at room temperature.
I prefer baking my Egg Muffin Cups in a ceramic muffin dish. But if you only have a regular nonstick muffin pan, that will work fine, too.
My mini frittatas did not overflow while they were baking but they were very full. Therefore, in case your muffin cups are slightly smaller than mine, I recommend placing the muffin pan on a foil-lined baking sheet the first time you make this recipe, to prevent a mess in the bottom of your oven just in case of overflow.
If your hash browns are heavily seasoned or contain a lot of sodium, you may want to use less salt the first time you make this recipe.
If you decide to use fresh shredded potatoes instead of a 16-ounce bag of frozen hash browns, you'll need about 3 cups total of shredded potatoes. Shred peeled potatoes into a bowl of cold water (to remove excess starch) and then drain well to remove all liquid. You also may need to add extra salt to this recipe if using freshly shredded potatoes.