You want French onion soup, but you don't want the soup. You want the flavors, that mix of salty, onion-y, and cheesy, but you want substance. Maybe a plate of rice stirred to creamy perfection might suit your fancy? And, why not, we'll throw some mushrooms on top, just to give this risotto a nice umami burst. Well, look at that, you've made for yourself exactly what you want.
Halve and peel onion. Slice halves into thin strips. Mince garlic. Stem thyme. Quarter mushrooms.
Caramelize the Onion
Make broth by bringing a small pot with 4 cups water and vegetable base to a boil. Place a medium pot over medium-high heat and add 2 tsp. olive oil. Add onion to hot pot and cook undisturbed, 4-5 minutes. Then stir occasionally until caramelized, 5-6 minutes. Transfer onion to a mixing bowl, and season with a pinch of salt and pepper. Reserve pot; no need to wipe clean. Cover bowl with plastic wrap.
Start the Risotto
Return pot used to caramelize onion to medium-high heat. Add 2 tsp. olive oil, garlic, thyme (reserve a pinch for garnish), and rice. Stir constantly until rice is lightly browned, 2-3 minutes. Add white wine and cook until absorbed, 30-60 seconds. Add 1 cup hot broth to pot with rice. Rice should just be covered by broth. Stir constantly until nearly all broth is absorbed.
Roast the Mushrooms
Place mushrooms on prepared baking sheet. Toss with 1 tsp. olive oil and a pinch of salt and pepper. Spread into a single layer and roast until tender and caramelized, 8-10 minutes. While mushrooms roast, finish risotto.
Finish the Risotto
Add another ½ cup broth and stir constantly until broth is nearly all absorbed. Repeat this process, stirring constantly, 18-20 minutes. Taste risotto as you cook, checking for tenderness. When rice has no more "bite" or crunch, it's done. There may be broth left. Remove pot from burner and stir in Parmesan cheese. Season to taste with salt and pepper.
Finish the Dish
Place risotto in a shallow bowl. Top with caramelized onions and mushrooms. Garnish with remaining thyme and Swiss cheese.