Preheat oven to 420°F.
Remove the stems from each mushroom and reserve them in a bowl. Using a small melon baller, gently scoop out some of the center of each mushroom to increase its capacity. Reserve the trimmings, with the stems, in the bowl.
Roughly chop the vegan sausage and pulse it in the food processor until ground. Add the sliced mushrooms and the reserved stems and trimmings, and pulse with the sausage until the mushrooms are minced.
Heat a large, nonstick sauté pan over medium heat, add the oil and wait until it shimmers. Add the mushroom-sausage mixture and sauté until the mushroom liquid has evaporated and the mushrooms are lightly browned. Season to taste with salt and pepper.
Transfer the mixture to a medium bowl and allow it to cool.