In a large saucepan, heat up olive oil and add half the diced garlic. Stir for 2 minutes, then add cauliflower. As soon as cauliflower softens, add in mushrooms. When the veggies are nearly done, add in the chard and stir until wilted. Season veggies with salt and pepper.
Transfer the cooked veggies into a bowl, and in the same pot, add the rest of the garlic. Stir for a minute or two, adding olive oil if needed.
Pour in the diced tomatoes with most of their liquid. While you wait for the tomatoes to heat through, begin boiling water for the pasta in a separate pot.
As soon as the tomatoes begin boiling, reduce the heat, and let simmer for 10 minutes. Add in the goat cheese and make sure it gets completely mixed in with the tomatoes. It should have a creamy consistency. As soon as it is heated through, add in the veggies.
When the pasta is finished cooking, drain, top with goat cheese sauce, and serve.