Heat a grill pan over high heat.
Coat the chicken in EVOO and season with salt and pepper. Grill for about 12 minutes, turning occasionally, then set aside.
Bring water in a saucepot to a boil for the pasta. Salt the water, add the pasta and undercook by 1 minute.
While the pasta cooks, melt 6 tablespoons butter in a separate saucepot. Spoon out half of the butter and toss with the panko breadcrumbs to moisten. Combine with half of the shredded Pecorino and reserve. To the remaining melted butter, add the garlic and anchovy paste and lots of coarse black pepper. Stir for 2 minutes, then whisk in the flour, then the stock, milk and Worcestershire sauce. Thicken until the sauce coats a spoon, then stir in the remaining half of the shredded Pecorino.
Drain the pasta. Halve the chicken breasts lengthwise, then thinly slice and combine with the pasta and sauce; transfer to a casserole and top with the breadcrumbs. Cool and store for make-ahead meal.
To reheat: Reheat, covered, in a hot 425°F oven to warm through, then uncover to brown.
Serve the Grilled Chicken Caesar Mac with shredded escarole or romaine lettuce and dress with lemon juice and EVOO.