Heat a large soup pot over medium heat. Pour in the olive oil and swirl it around. Add all of the sliced onions to the pot. You should hear a moderate sizzle. Sauté the onions, stirring often, until they are just starting to soften on the edges. Then, lower the heat slightly.
Keep cooking and stirring the onions occasionally until they are light golden brown, jammy, and super sweet. Not quite in the caramelized state, but getting there. This process will take anywhere from 45 minutes to an hour. Add splashes of water if the onions start to dry up/stick.
Increase the heat back to medium. Add the thyme, bay leaf, and garlic to the pot and stir until fragrant, about 30 seconds. Add the tomato paste and stir. Cook for about one minute. Add the lentils to the pot and stir. Then, add the sherry vinegar and tamari to the pot. Scrape up any browned bits on the bottom of the pot. Season everything with salt and pepper. Add the vegetable stock to the pot and stir once more. Cover the pot and bring it to a boil. Lower the heat to a simmer and then cook until lentils are tender, about 25-30 minutes. There should be just enough liquid to surround the onions and lentils. Add more vegetable stock if necessary.
Remove the bay leaf from the pot and allow the French onion base to cool slightly before transferring to a large (12-inch), oven-safe skillet or other baking dish. Set aside.
Make the creamy cauliflower potato mash. Pour the water into a large soup pot and bring it up to a boil. Pop the smashed garlic cloves in the water. Place the potatoes and cauliflower either directly into the pot or in a steamer insert. Keep the water at a strong simmer and close a lid on top of the pot. Steam the cauliflower and potatoes until the potatoes are fork-tender, about 20 minutes.
Drain the vegetables and return them to the pot. You can keep the garlic or toss it, your choice! Add the vegan butter, non-dairy milk, nutritional yeast, and lots of salt and pepper. Using a hand masher, mash the cauliflower and potatoes until smooth and creamy. Adjust the seasoning if necessary and set aside.
Preheat the oven to 375°F.
Transfer the French onion and lentil base to an oven-safe skillet or other baking dish. Smooth the French onion and lentil base out. Then, dollop the creamy cauliflower and potato mash on top. Carefully spread the mash out over the surface of the French onion and lentil base. Drizzle the top of the mash with olive oil and some extra pinches of salt and pepper.
Bake the French onion shepherd’s pie for 25 minutes, or until bubbly and totally heated through. You can broil the top for extra browning if you like. Remove the pie from the oven and let it sit for 5 minutes before serving in shallow bowls.