Heat the oven to 375°F. Lightly grease a loaf pan or line a rimmed baking sheet with parchment.
Warm the olive oil in a skillet over medium heat. Add the chopped mushrooms and cook for 5 to 7 minutes, stirring occasionally, until tender and their released moisture has mostly evaporated. Set aside to cool slightly.
In a large bowl, whisk together the egg and milk. Stir in the stuffing mix and let it soften for 2 minutes. Add the ground turkey, cooked brown rice, mushrooms, black pepper, and 3/4 cup of the Swiss cheese.
Mix gently until the ingredients are just combined. Transfer the mixture to the prepared loaf pan or shape it into a loaf on the parchment-lined baking sheet. Avoid packing it tightly, which can make the meatloaf dense.
Bake for 40 minutes. Sprinkle the remaining 1/4 cup Swiss cheese over the top and bake for another 10 to 15 minutes, until the center reaches 165°F.
Let the meatloaf rest for 10 minutes before slicing. This helps the slices hold together with the brown rice and melted cheese.