In a heatproof bowl, cover the porcini with 1 cup of boiling water. Let stand until softened, about 20 minutes. Lift the mushrooms from the soaking liquid and coarsely chop them. Let the soaking liquid stand to settle.

Meanwhile, preheat the oven to 375 degrees and set a rimmed baking sheet on the center rack. In a bowl, combine the garlic, cheese, sage and rosemary. On a work surface, pound the steak 1/2 inch thick and season with salt and pepper. Spread the herb mixture on one side of the steak and roll it up lengthwise, with the grain; tie with string at 1-inch intervals.

In a large skillet, heat the oil. Add the steak and cook over moderately high heat until browned, 8 minutes. Transfer to the hot baking sheet and roast for 20 minutes, until a thermometer inserted in the thickest part registers 125 for medium-rare. Let the steak rest for 5 minutes and remove the strings.

Meanwhile, wipe out the skillet. Add the porcini and red wine; simmer over moderately high heat until the wine has reduced by one-third, 2 minutes. Gradually add the porcini liquid, stopping before you reach the grit at the bottom of the bowl. Whisk the broth with the cornstarch, then add to the skillet; simmer over low heat until the sauce is thickened, 3 minutes. Season with salt and pepper.

Thinly slice the steak crosswise, garnish with the parsley and serve with the sauce.