Remove the outer leaves from the cabbage and discard them.
Cut the cabbage in half and remove the core.
Slice the cabbage into thin ribbons about ¼ inch wide.
Heat the olive oil and butter together in a large wide skillet over medium heat.
Add the sliced cabbage to the skillet and spread it out evenly.
Cook the cabbage for 8 to 10 minutes, stirring occasionally, until tender with lightly browned edges and most moisture has cooked off.
Add the minced garlic to the skillet and cook for 30 seconds until fragrant.
Reduce the heat to medium-low.
Pour in the heavy cream and milk and stir to combine with the cabbage.
Simmer gently for 5 minutes, stirring often, until the sauce begins to thicken.
Add the Parmesan cheese and stir until melted and smooth.
Season with salt, black pepper, Italian seasoning, nutmeg, and red pepper flakes if using.
Continue cooking for 2 to 3 minutes, stirring gently, until the sauce coats the cabbage evenly and looks glossy.
Taste and adjust seasoning if needed.
Serve immediately while hot.