Preheat the oven to 350 degrees F. Butter a 9-by-9-inch baking dish.
Bring a medium pot of salted water to a boil. Slice the cabbage into 4 wedges. Remove the hard inner core. Parboil the wedges for 1 to 2 minutes. Drain very well, then arrange in the prepared baking dish.
In a medium skillet over medium heat, melt the butter. Whisk in the flour and cook for a minute or 2. Whisk in the milk, add a pinch of salt and pepper and cook until beginning to thicken. Turn off the heat and stir in the processed cheese and pepper Jack.
Pour the cheese mixture over the cabbage. Dot with the jalapeno rounds and sprinkle on some paprika. Bake until golden and bubbly, about 20 minutes.