Start by grinding 1-2 tablespoons of black pepper corns
Brush the tops and bottoms of the mushroom caps with olive oil until fully coated.
Using your hands, gently press the ground black pepper into the top of the mushroom caps as well as into the gills on the bottom.
Get your stainless steel or cast iron pan very hot, then add enough olive oil to coat the pan.
Once hot, but not smoking, place the mushroom caps top-side down. Allow this to sear for about 1 minute, while gently pressing down with a spatula.
After the minute, flip the mushrooms and press down again with a bit more pressure to slightly flatten the mushroom caps. Cook for 2 minutes.
If necessary, repeat these steps until the mushrooms are cooked all the way through. They will appear much darker and softer when cooked through.
Once cooked, remove mushroom caps from the pan, but keep the pan warm and on the stove.
Place the mushroom caps on a plate and allow them to rest for about 5 minutes while making the sauce.
With the pan on medium heat, add ½ tablespoon of ground pepper. With a spatula, stir this around the pan to lightly toast.
Add cognac to the hot pan and scrape the bottom of the pan to get all of the bits of pepper and flavor up. Allow the cognac to simmer and reduce.
Add vegan butter and stir.
Once the cognac and butter has mostly reduced, whisk in 2 tablespoons of flour until a thick paste forms.
Then, whisk in 1 ½ cups of non-dairy milk slowly. Whisk this in ½ cup at a time.
Allow this sauce to come to a simmer and thicken to your liking. Season with salt and extra pepper if you would like.
Plate the mushroom caps and spoon the pepper sauce over the top of them.