Preheat the oven to 375 degrees F; butter a shallow 3-quart baking dish. Melt 2 tablespoons butter in a large nonstick skillet over medium-high heat. Add the mushrooms, season with salt and cook, stirring occasionally, until tender and lightly browned, 8 to 10 minutes. Transfer the mushrooms to a plate and wipe out the skillet.
Melt 6 tablespoons butter in the same skillet over medium heat. Add the leeks; cook, stirring occasionally, until tender, about 6 minutes. Add the mushrooms, thyme, rosemary, broth, 1 teaspoon salt and a few grinds of pepper. Bring to a simmer, then remove from the heat.
Whisk the eggs and heavy cream in a large bowl. Add the herbs, bread cubes and mushroom-broth mixture and stir until combined. Transfer the stuffing to the prepared baking dish. Cut the remaining 2 tablespoons butter into small cubes and scatter evenly over the stuffing. Cover with foil and bake 30 minutes, then uncover and bake until golden, 20 to 30 more minutes.
Photograph by Ryan Dausch