In a small saucepan, melt 4 tablespoons of the butter. Cook over moderate heat until deep golden, 4 to 5 minutes. Keep warm.
In a medium skillet, melt 4 tablespoons of the butter. Add the mushrooms, 2 tablespoons of the shallots and the garlic and season with salt. Cook over moderately high heat, stirring occasionally, until the mushrooms are golden and tender, 3 to 4 minutes. Transfer to a plate and keep warm.
In a bowl, beat the heavy cream until soft peaks form; refrigerate.
In a medium saucepan, heat the grape seed oil. Add the remaining 1/4 cup of shallots and cook over moderate heat, stirring occasionally, until translucent, about 2 minutes. Add the rice and cook, stirring, for 2 minutes. Add the vermouth and cook until almost evaporated, then stir in the wine and cook until almost evaporated, about 2 minutes. Add 1/2 cup of the hot water and cook, stirring constantly, until the liquid is absorbed, about 2 minutes. Continue stirring in hot water, 1/2 cup at a time, until it is almost absorbed before adding more. The risotto is done when the rice is just al dente, about 18 minutes total. Stir in the lemon juice, grated cheese and the remaining 2 tablespoons of butter.
Fold the whipped cream into the risotto and bring to a simmer for 30 seconds; the risotto should be thick and frothy. Season with salt. Spoon the risotto into bowls and drizzle with the browned butter. Top with the caramelized mushrooms, garnish with thyme, grated lemon zest and cracked pepper and serve at once.