This is a meatless dish, but not a vegetarian one — the meat is on the side. If you prefer, you can substitute large shiitake mushrooms, porcini, and thick slices of puffball mushrooms for the portobellos.
Prepare the grill and let it burn down to medium-hot coals. While waiting for the grill to be ready, make the sauce. Heat 1 tablespoon of the olive oil in a medium saucepan over medium-high heat until hot. Add the shallot and cook briefly until soft and light brown. Add 1 teaspoon of the thyme and stir. Then add the red wine, bring to a boil, and cook until reduced to about 1/4 cup. Add the stock, return to a boil, and continue to cook until reduced to about 3/4 cup. Season with salt and pepper.
Measure 2 tablespoons sauce into a medium bowl and whisk in the red wine vinegar. While whisking rapidly, drizzle in 1 tablespoon of the olive oil. Taste for salt and pepper. Set the vinaigrette aside until ready to assemble the dish. Whisk the butter into the remaining sauce, season with salt and pepper to taste, and keep warm.
In a medium bowl, whisk together the remaining 1/2 cup olive oil, the balsamic vinegar, the garlic, and the remaining 1 teaspoon thyme. Holding the mushrooms one at a time over the bowl, spoon the marinade over them and let the excess run back into the bowl. Repeat until the mushrooms have been well coated all over. (This method prevents the mushrooms from absorbing too much marinade.) Lay the mushrooms on a plate and season both sides with salt and pepper.
Place the mushrooms, gill side down, on the grill and cook, turning once, until browned on both sides and cooked through, about 4 minutes total. Remove and keep warm.
Add the spinach to the vinaigrette and toss well. Divide the potatoes among 4 warm plates. Top with the mushrooms, gill side up, and spoon the sauce onto the mushrooms and over the potatoes. Top with the spinach salad and serve immediately.
Chef's Note:
If the olive oil flares up and burns the mushrooms, it creates a petroleum flavor. So make sure the oil doesn't drip from the mushrooms when you put them on the grill. If you don't care to start the grill, you can cook the mushrooms indoors on a ridged stovetop grill. Oil it lightly and preheat it before cooking the mushrooms. Or you can use a heavy sauté pan or our bistecca pan with a little olive oil, preheated over medium-high heat, then turned down to medium to cook the mushrooms through.
