Place the first 7 ingredients in a medium bowl and whisk to combine.
Combine the stock, water and lemon juice in a pot and bring to a simmer. Add the mushrooms and simmer until just tender, about 2 to 3 minutes. Drain the mushrooms well, place in the bowl with the vinaigrette, and toss to combine. Cool the mushrooms to room temperature, and then cover and refrigerate until needed. (Mushrooms can be made up to a day in advance of serving.)
Preheat your grill to medium-high. Brush the steaks with the 1 Tbsp. oil and season with salt and pepper. Grill the steaks to the desired doneness, allowing approximately 2 to 3 minutes per side for rare to medium-rare, and 3 to 4 minutes per side for medium. Plate the steaks and serve with the mushrooms.