Dry sauté the mushrooms in the oil. Brown the mushrooms lightly but don’t let them get too dark, as they will be cooked again. Set aside to cool.
Grate the potatoes into a large mixing bowl. Mix in the onion, salt, and black pepper, and set aside.
Chop the mushrooms into ¼-inch (6 mm) pieces. Use your hands to squeeze out as much moisture as possible from the potato and onion mixture, and drain out the water. Mix the mushrooms into the potato and onion mixture, then add the matzo meal, stirring to coat everything evenly.
Heat a large heavy-bottomed pan over medium heat. When hot, add 1 tablespoon of oil.
Using your hands, grab a handful of the shredded mixture, form a ball, then press it into a round, flat pancake shape. Press it tight and flat between your hands to squeeze out as much liquid as possible. You want the latke to be about ⅜ inch (1 cm) thick when you are done. Place the latke into the pan. Repeat until the pan is full, but leave at least 1 inch (2.5 cm) between the latkes. Add 1½ tablespoons of butter to the space between the latkes. Do not move the latkes until they are ready to be flipped. When the bottom of the latke is crispy and golden brown, 4 to 5 minutes, carefully flip it and gently press on the top to get a nice flat surface on the bottom.
When the second side is crispy and golden brown, another 4 to 5 minutes, transfer to a cooling rack or plate lined with paper towels to drain any extra fat, and sprinkle with a small pinch of salt. Repeat until all latkes are cooked, adding more oil and fat to the pan as needed. Keep the cooked latkes uncovered in a 200° F (95°C) oven.
