Bring 6 cups vegetable stock to a steady, slow simmer in a saucepan. Take into account how salted it is and adjust the rest of the salt you use in the mushrooms and the risotto.
Heat 2 tablespoons unsalted butter and 2 tablespoons olive oil in a heavy pan over moderate heat.
Add ⅓ cup green onions, sprinkle ⅛ teaspoon salt, and sauté for 1 or 2 minutes, until beginning to soften, being careful not to brown them.
Add 2 cups risotto rice with 1 teaspoon thyme leaves and, using a wooden or silicon spoon, stir for 1 minute, stirring constantly, making sure the grains are very well coated.
Pour ½ cup white wine, stir once and cook until it's almost absorbed.
Add ½ cup of broth and half of the reserved mushrooms. Stir well, reduce the heat to medium/low and cook until the liquid is almost absorbed. Then continue adding simmering broth, ½ cup at a time, and cook until it's almost absorbed before adding the next one. Stir frequently, so that the rice releases the starch and turns into a creamy mixture.
Risotto takes 18 to 20 minutes to cook al dente, which means tender but still firm.
Remove the pan from the heat and immediately add the reserved 4 tablespoons unsalted butter, ⅓ cup grated Parmesan cheese, and 2 tablespoons chopped fresh parsley. Stir vigorously to melt the butter and integrate with the rice. Add pinch black pepper, check for salt, and add more if needed.
Transfer to a serving platter, mound the remaining mushrooms on top, 1 tablespoon chopped green onions or parsley, a drizzle of olive oil and serve immediately. Risotto waits for no one.