Lay the block of tofu on a few paper towels. Top the tofu with a few more paper towels and set something moderately heavy (see the owl pictured) on top of the paper towels to weigh it down. Allow to drain for 15 minutes then cut into 1/4-inch rectangles. While the tofu is draining, feel free to get the rest of the dish prepped.
Preheat the oven to 400 degrees F. To a small baking sheet or roasting pan, add the mushrooms. Drizzle a teaspoon or two of olive oil over the mushrooms and sprinkle with a few pinches of salt. Transfer the mushrooms to the oven and cook for 10-12 minutes, until tender and slightly golden brown. Set aside.
Place a skillet over high heat and add about 1/4-inch of olive oil. When the oil is hot, carefully add the tofu, cooking them on each side for about 2-3 minutes and until they're lightly golden brown. Remove and drain on a paper towel. Set aside.
Set a medium pot over moderately high heat. Add 2 cups of water and one tablespoon of the miso paste. Mix until the paste is completely dissolved and the broth begins to boil. Once it reaches a boil, turn the heat to low. Salt the broth to taste (I added about 1/2 teaspoon). Also, if you want the miso bolder, you can adjust the amount too. Next, add the mushrooms, watercress and fresh peas; cook for an additional minute.
To serve, divide the slices of tofu between two bowls. Ladle the miso soup over the tofu and garnish with a few slivers of green onion.