1. Place porcini in a bowl. Cover with 2 cups boiling water; let sit until softened, about 20 minutes. Remove from liquid. Finely chop, and set aside. Strain liquid through fine cheesecloth or a coffee filter, discarding grit; set aside.

2. Place orzo in a large skillet over medium-low heat. Toast, stirring continuously, until light golden, about 6 minutes. Remove from heat; set aside.

3. Bring a pot of water to a boil; add toasted orzo; cook until al dente, 3 to 4 minutes. Drain, and set aside.

4. Warm olive oil in a stockpot over low heat. Add Vidalia onion, yellow onion, shallot, and thyme; cook, stirring occasionally, until onions are very soft and golden brown, 45 to 50 minutes. Increase heat to medium; add cremini mushrooms; saute, stirring frequently, until mushrooms have softened and browned, about 8 minutes. Add Madeira; cook 1 minute more. Add reserved porcini, reserved strained liquid, beef stock, salt, and pepper; bring to a simmer. Add reserved pasta; continue to cook until pasta is heated through, about 2 minutes more. Serve immediately, garnished with chopped parsley.