Preheat oven to 400°F.
Toss the asparagus pieces in the oil and sprinkle with ¼ tsp salt and ¼ tsp pepper.
Place the asparagus on a baking sheet and roast in the oven for 10 minutes. Set aside.
Liberally grease the soufflé dish (or ramekins) with butter. Sprinkle the Parmesan cheese all over the insides and bottom of the dish. It's okay if there is excess in the bottom of the dish.
In a medium saucepan, heat the butter over medium-low heat. Add the flour and whisk to fully incorporate. Cook for 1 to 2 minutes. Don't let it begin to brown.
Slowly whisk in the warmed milk, and bring to a simmer, or boil. Continue whisking and cooking until very thick, about 3 to 5 minutes.
Remove from heat and mix in the cheese, Dijon, chives, ½ tsp salt, and ¼ tsp of black pepper.
Gently stir in the egg yolks one at a time. Making sure they are fully incorporated before adding the next yolk.
In a large bowl (metal or glass), add the egg whites with a pinch of salt. Use a hand mixer on high to beat them until soft peaks just form. Don't over-beat them!
Add about ⅓ of the egg whites to the yolks/cheese mixture and gently fold them with a wooden spoon or whisk. Add the remaining whites and fold together until just combined. Don't overwork the mixture (it's okay if some white streaks are visible).
Transfer the asparagus into the bottom of the dish and then pour in the egg mixture, using a spatula to gently smooth the top.
Place the dish in the oven (400°F) and bake for 27 minutes.
Remove from oven and serve immediately.