In a 12-inch frying pan with 2-inch-tall sides or a 5-quart pan over medium-high heat, stir bacon until browned and crisp, about 5 minutes. Transfer to paper towels to drain. Discard all but about 1/2 tablespoon bacon fat from pan.
Add 2 tablespoons olive oil to pan over medium-high heat. When hot, add onion, garlic, salt, and pepper. Reduce heat to medium and stir frequently until onion is very soft and browned, 20 to 25 minutes (if onion starts to scorch, reduce heat further and stir in 2 tablespoons water).
Meanwhile, rinse chard. Trim and discard stem ends. Thinly slice stems crosswise and coarsely chop leaves. In a 5- to 6-quart pan over high heat, bring about 3 quarts water to a boil. Add chard and cook, stirring occasionally, until stems are tender-crisp to bite, 3 to 4 minutes. Drain, place in a large bowl of ice water until cool, and drain again.
Add rice to onions and stir until opaque, about 3 minutes. Add wine and stir over medium heat until absorbed, 1 to 2 minutes. Add 6 cups broth, a cup at a time, stirring after each addition until almost absorbed, 20 to 25 minutes total (rice should be tender to bite).
Stir in cheese, butter, bacon, chard, and roasted mushrooms. If risotto is thicker than desired, stir in a little more broth. Spoon risotto into wide, shallow bowls.