Set a large pot of salted water over high heat and allow to come to a boil.
Set a large sauté pan over medium-high heat and swirl the oil into it. When the oil shimmers, add the bacon and cook, stirring occasionally, until it is beginning to crisp, 5 to 7 minutes. Remove the bacon to a plate and pour off all but a healthy tablespoon of fat.
Add 2 tablespoons of the thyme and the garlic to the pan and fry them, stirring frequently, until they are fragrant and softening, 2 to 3 minutes, then add the parsnips and lower the heat to medium. Cook the parsnips, stirring occasionally, until they are soft and caramelized, about 10 minutes, then return the bacon to the pan and stir. Turn the heat to low and stir occasionally until you’re ready to use it.
Meanwhile, cook the pasta in the boiling salted water until it is just al dente, probably a minute or so less than the instructions on the packaging, then fish out a cup of the pasta water and drain the rest.
Put the pasta in a large, warm serving bowl and add to it the parsnips and bacon, along with the butter and cheese, and toss to combine. Add a few splashes of the reserved pasta water to loosen everything up and give the pasta a sheen. Season to taste with salt and pepper. Sprinkle the remaining 1 tablespoon thyme over the top of the pasta and serve.