In a small saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1 minute. Gradually whisk in the warmed almond milk and cook, whisking, until steaming hot and thick, about 6 minutes. Remove from the heat and stir in the garlic and cheese until the cheese is melted, then season to taste with salt and pepper. Stir in half of the broccoli florets until coated.
Meanwhile, preheat the oven to 375 degrees F. Place 2 (uncoated) broccoli florets in the center of each chicken piece and roll up to seal. Transfer half of the cheese sauce to a 6-cup glass baking dish and arrange the chicken roll-ups, seam-side down, on top. Cover with the remaining cheese sauce and bake until cooked through, about 30 minutes.
To eat now: Slice each chicken roll-up crosswise, arrange on 4 plates and drizzle with cheese sauce.
To freeze and eat later: Cover the glass baking dish with a tight-fitting lid and freeze up to 1 month. To thaw, place in the fridge overnight. Cover with foil and bake in a 400 degree F oven until heated through, about 20 minutes.