First, preheat your oven to 400 °F (200 °C). In a large pot of lightly salted boiling water, cook the tortellini uncovered. When they float and the filling is hot (about 3–5 minutes), drain and transfer into your baking dish.
In a skillet over medium heat, warm the canola oil and cook sliced mushrooms until golden (12–15 min). Add butter until melted, then whisk in flour until mixture lightly browns (about 1 minute).
Slowly pour in milk, stirring constantly to avoid lumps, and bring to a gentle bubble (7–8 min). Season with salt and pepper, remove from heat, then stir in grated Parmesan. Pour this creamy sauce over the tortellini in your baking dish.
Bake in your preheated oven until the top just starts to brown, about 20–25 minutes. Let it rest briefly, then serve immediately while hot and gooey.