Heat the olive oil in a large Dutch oven over medium heat. Season the chicken thighs with salt and pepper, then brown them on both sides for about 4 minutes per side. Remove the chicken and set it aside.
Add the diced onion and minced garlic to the pot. Cook for 3 minutes until the onion softens.
Stir in the sliced carrots, sliced parsnips, and cubed potatoes. Cook for another 3 minutes, stirring occasionally.
Pour in the beer and scrape the bottom of the pot to loosen any browned bits. Let the beer simmer for 2 minutes.
Return the chicken thighs to the pot. Add the chicken broth and dried thyme. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 45 minutes.
Remove the lid and simmer uncovered for 10 more minutes to thicken the broth slightly. Taste and adjust salt and pepper if needed. Sprinkle with chopped fresh parsley before serving.