Combine 1 Tbsp. salt and 10 cups water in a medium pot. Bring to a boil, then reduce heat to medium to maintain a bare simmer.****
Meanwhile, heat oil in a 6-qt. Dutch oven over medium. Add onion and a pinch of salt and cook, stirring often, until onion is translucent and starting to soften, 6–8 minutes. Add ½ cup water and cook, stirring often, until water evaporates and onion is sizzling in oil and tender, about 5 minutes. Taste onion; if it’s still firm at all, add a splash of water and continue to cook until meltingly soft.
Add rice and stir well to coat with oil. Cook, stirring constantly, until grains are translucent around the edges and make a clattering sound when they hit against the pot, about 5 minutes. (Coating grains with oil before adding any liquid helps the rice cook evenly so that the outside does not become mushy before the center is tender.) Add wine and another pinch of salt. Bring to a simmer and cook, stirring occasionally, until wine evaporates, about 2 minutes.
Reduce heat to medium, then add hot salted water to rice in ¾-cup increments, stirring constantly and allowing liquid to absorb fully before adding more, until rice is al dente and suspended in a fluid, not-too-thick creamy liquid, 25–30 minutes. It should take 2–3 minutes for each addition to be absorbed; if things are moving faster than this, reduce heat to medium-low. Gradual absorption and constant agitation are key to encouraging starches to release from risotto, creating its trademark creamy consistency. You may not need all of the hot water, but the finished texture should be more of a liquid than a solid. Start checking rice about 15 minutes after the first water addition; the grains should be tender but not mushy, with a slightly firm center that doesn’t leave a chalky residue between your teeth after tasting. Do not overcook! Only add more liquid once the previous ladleful has been absorbed.
Remove pot from heat, add butter, and stir until melted. Gradually add Parmesan, stirring until cheese is melted and liquid is creamy but very loose; stir in more hot salted water if needed. Taste and season with more salt.
Heat oil in a large skillet over medium-high until shimmering. Add mushrooms; cook, tossing occasionally, until they begin to soften and release some liquid, about 3 minutes. Season with salt and pepper; cook, tossing occasionally, until deeply browned and tender, 8–10 minutes. Add thyme, garlic, and butter and cook, tossing occasionally, until garlic softens and butter is golden brown, about 3 minutes. Remove from heat and add vinegar. Toss to coat, scraping up any browned bits. Pluck out thyme.
Divide risotto among warm bowls. Top each with a few grinds of pepper and spoon mushroom mixture over. Serve with Parmesan alongside.