Bring a large pot of water to a boil. Salt lightly if desired because the miso adds salt. Cook the linguine until just short of the package's al dente time. Before draining, reserve 1 cup of the cooking water.

Meanwhile heat the olive oil and 1 tablespoon butter in a wide skillet over medium-high heat. Add the mushrooms in two batches if necessary. Cook for 8–12 minutes, stirring occasionally, until their released liquid has evaporated and the surfaces are golden brown. Lower the heat if the pan starts to scorch.

Reduce the heat to medium-low. Stir the garlic, pepper and optional thyme into the mushrooms and cook for about 30 seconds until fragrant.

In a small bowl whisk the miso with 1/3 cup hot pasta water until smooth. Add it to the skillet with the remaining 2 tablespoons butter. Stir gently over low heat; do not boil vigorously.

Add the drained pasta and toss for 1–2 minutes, adding reserved water a tablespoon at a time until the sauce coats the noodles lightly and they separate easily. Remove from the heat. Add lemon juice and scallions. Taste before adding any salt. Finish with optional sesame and serve immediately.