Steam cauliflower until fork-tender (don't let it get mushy). Remove from heat and set aside to cool.
In a medium size bowl, beat the egg and whisk in the milk until combined. Gradually add in the flour and salt and continue whisking until a batter is formed.
Add parsley and butter and stir until combined. Set aside.
Chop the steamed cauliflower into small bite-sized pieces.
Fold the cauliflower into the batter until well combined. Set aside.
Pour olive oil into a 9-inch cast iron skillet until it's about a ¼ inch high. Heat over medium-high heat.
Once the oil is very hot, reduce the heat to medium, and add spoonfuls of the batter (2 tablespoons per fritter) to the pan in batches of 4-5. Cook until golden brown, about 3-4 minutes per side.
Remove fritters with a slotted spatula or spoon and place on a plate lined with paper towels. Sprinkle with a little more salt if desired.