Heat the oven to 375°F (190°C) and lightly oil a standard loaf pan or an 8-inch baking dish. If you are starting with dry lentils, simmer 3/4 cup in salted water until just tender, 20 to 25 minutes, then drain them well.

Warm the olive oil in a large skillet over medium heat. Add the onion, carrot, and celery with a pinch of salt and cook, stirring, until softened, about 6 to 8 minutes. Add the mushrooms and cook until they release their liquid and start to brown, about 6 minutes more.

Stir the rolled oats into the skillet and toast them with the vegetables, stirring often, until they smell nutty and pick up a little color, 3 to 4 minutes. Sprinkle in the black pepper, allspice, nutmeg, and thyme and stir for 30 seconds so the spices bloom in the oil.

Pour in the vegetable broth and soy sauce, add the yeast extract, and stir until it dissolves. Fold in the cooked lentils and cook for 2 to 3 minutes until most of the liquid is absorbed and the mixture looks thick and cohesive. Taste and add more salt if it needs it.

Pack the mixture firmly and evenly into the prepared dish, smoothing the top. Bake for 45 to 50 minutes, until firm around the edges and well browned on top. Let it rest for 10 minutes so it sets, then slice and serve.