Preheat the oven to 375 degrees . Arrange the bacon on a slotted broiler pan or on a rack placed over a baking sheet and bake until crisp, about 15 minutes. Chop and reserve. Switch on the broiler and position the rack in the center of the oven.
Bring a pot of water to a boil, salt it, add the pasta and cook 1 minute less than the instructions indicate, or until just shy of al dente. Drain and return to the pot.
While the pasta is working, heat a grill pan or cast-iron griddle over medium-high heat. Drizzle the chicken with EVOO to coat lightly, then season evenly with the paprika, salt and pepper. Grill the chicken for about 10 minutes, turning occasionally. Transfer to a cutting board and halve the pieces lengthwise, then thinly slice crosswise.
While the chicken cooks, melt the butter in a medium saucepan over medium heat. Add the onion and cook until light golden and very soft, 15 to 20 minutes. Sprinkle in the flour and stir for 1 minute. Whisk in the cider (or stock), then the milk. Bring to a boil and cook, whisking, until the sauce coats the back of a spoon, 3 to 4 minutes. Add the thyme and season with salt, pepper and nutmeg. Stir in the cheeses until melted.
Add the chicken, bacon and sauce to the pasta and transfer to a casserole. Broil until bubbling and browned, about 5 minutes. Garnish with the parsley (or celery greens).