Get out a large skillet with deep sides and heat the olive oil in it over medium high heat. Cook the broccoli, onion, garlic and sage in it for 3-4 minutes to let them start to soften. Then add in the diced chicken and let it cook through completely for another 3-4 minutes. While it cooks, season the mixture generously with salt and pepper. When the chicken is cooked, add in the white wine and let everything simmer in the wine for another 4-5 minutes. The wine should almost cook off completely with just a little left in the bottom. Remove everything from the pan and transfer it to a plate. Set it aside and start on the sauce.
Add the butter and flour to the pan and whisk them together until you have a thick, golden paste. Slowly add in the milk while you keep whisking until you have a smooth sauce. Then whisk in the mustard, nutmeg and an extra pinch of salt. Let the sauce gently bubble and thicken for 10 minutes, whisking it occasionally. Meanwhile, bring a large pot of water to a boil and cook the pasta shells in it until tender, about 7-8 minute. Drain them and lay them out on a clean surface to let them cool enough to handle.
When the sauce is done, take half of the grated cheese and whisk it in until smooth. Take the pan off of the heat. Get out a large 9 x 13 pan and pre-heat the oven to 350. Spread half of the cheesy sauce into the bottom of the baking pan. Then pour the chicken and broccoli mixture into the skillet of remaining sauce and stir it all together well to make the filling. Generously fill all of the shells with the filling and lay them out in a single layer in the baking dish. Then take the remaining half of grated cheese and sprinkle it evenly on top of each shell. Bake the shells just to melt everything and make it bubbly for 10-15 minutes. Serve immediately and enjoy!