Mushroom-Steak Diane

Stir together broth, soy sauce, mustard, miso paste, and red pepper in a small bowl.

Cut mushrooms in half lengthwise. Score the inside of each mushroom half with shallow diagonal cuts (do not cut all the way through). 

Heat 2 tablespoons oil in a large cast-iron or nonstick skillet over high heat, swirling to coat bottom. Cook mushrooms, cut sides down, until bottoms are golden brown, 3 to 5 minutes (do not stir). Reduce heat to medium. Pour half of broth mixture (about 1/3 cup) into skillet. Cook, covered, until liquid is mostly absorbed and mushrooms are fork-tender, about 5 minutes. (Add water as needed, 2 tablespoons at a time, if liquid evaporates and mushrooms are not yet tender.) Transfer mushrooms to a bowl.

Add remaining 1 teaspoon oil and the shallot to skillet. Cook, stirring constantly, over medium heat 30 seconds. Add sake; bring to a boil over high heat. Cook, stirring frequently, until slightly reduced, about 1 minute. Add coconut milk, remaining broth mixture, and any accumulated juices from mushrooms. Cook over high heat just until sauce starts to thicken, about 2 minutes. 

Return mushrooms to skillet. Reduce heat to low. Gently simmer until mushrooms are heated through, adding water as needed, 1 tablespoon at a time, until sauce reaches desired consistency, about 2 minutes. 

Serve mushrooms over lentils and top with sauce and chives.