Heat oil in a pot or Dutch oven over medium-high heat. Add shallot slices and saute for 1 minute, then add garlic and mushrooms. Saute until mushrooms start to soften, about 3 minutes, stirring frequently so garlic doesn't burn. Add vegetable stock, thyme, and salt and increase heat to high. Bring to a boil, stirring occasionally.

Stir in lentils and sesame oil, and reduce heat to a simmer. Simmer, stirring occasionally, until lentils are tender, about 20 minutes.

Divide soup between 4 bowls and garnish with sliced green onions.