Heat olive oil in a large pot over medium heat.
Sauté onion and garlic until fragrant and translucent.
Add carrots, celery, and potatoes. Stir for 5 minutes.
Pour in vegetable broth and bring to a boil.
Reduce heat and simmer until vegetables soften (about 25 minutes).
Stir in lentils and thyme, season with salt and pepper. Simmer 5 minutes more.
Meanwhile, whisk cornstarch with a little plant milk until smooth.
Heat remaining plant milk with coffee and sugar in a saucepan.
Slowly add cornstarch mixture, stirring until pudding thickens. Remove from heat and stir in vanilla.
Serve soup hot with a small side of coffee pudding for dessert.