In a large saucepan, combine the rice, 3 cups broth, ½ cup water and a pinch of salt. Bring to a vigorous simmer over medium-high and cook, uncovered and stirring occasionally, until the rice has absorbed all of the liquid, 15 to 20 minutes.
Meanwhile, in a 12-inch skillet over medium, melt 2 tablespoons butter. Add the shallots, thyme and ¼ teaspoon salt; cook, stirring, until the shallots are translucent, 3 to 4 minutes. Add the wine and simmer over medium-high, stirring, until almost fully reduced, 3 to 4 minutes. Set aside off heat.
When the rice has absorbed the liquid, scrape it into the skillet. Stir, then bring to a simmer over medium-high. Add about ⅓ cup of the remaining broth; cook, whisking vigorously, until the rice has absorbed the liquid and begins to stick to the pan, about 2 minutes. Repeat with the remaining broth in two additions. The rice should be creamy and al dente.
Off heat, whisk in ¼ cup water, the cheese and the remaining 1 tablespoon butter. Cover and let stand 5 minutes. If desired, thin with additional water, then taste and season with salt and pepper. Serve immediately, sprinkled with additional Parmesan and thyme.
