Melt 1/2 tablespoon of the butter with 1/2 tablespoon of the olive oil in a heavy large skillet over medium-high heat. Add ½ of the mushrooms and sauté for 3-4 minutes until browned. Remove the mushrooms from the pan and set aside.
Repeat with the remaining mushrooms using the other ½ tablespoon of butter and a ½ tablespoon of oil. Bring 4 cups vegetable broth to a simmer in a medium saucepan; keep warm.
Heat the remaining 2 tablespoons of olive oil in large saucepan over medium-low heat. Add the leek, thyme, salt, and pepper. Sauté the leek until tender (about 4 to 5 minutes). Add the rice and increase the heat to medium.
Stir until the edges of the rice begin to look translucent (about 3 to 4 minutes). Add the white wine and stir until the liquid is absorbed (about 1 minute). Add 3/4 cup of warm broth; stir until almost all the broth is absorbed (about 1 minute).
Continue adding broth by 3/4 cup, stirring until almost all the broth is absorbed before adding the next ¾ cup. Continue until the rice is cooked (about 20 minutes). Stir in the mushrooms and stir to heat through.
Remove from the heat and fold in the Parmesan and cottage cheese. Serve immediately. Refrigerate leftovers.