Preheat your oven to 425 degrees F. Move an oven rack into the top position available.
Peel the carrots and parsnips and remove the ends. Then cut them into 1/2-inch thick pieces on the bias (AKA diagonally).
Place the veggies on a baking sheet. Drizzle generously with olive oil and season with salt and pepper. Use your hand to toss the veggies so they're evenly coated. Spread them into a single layer.
Roast for 20-25 minutes on the top rack of your oven. Once ready, the veggies will be tender, starting to brown around the edges, and caramelized on the side touching the baking sheet.
When there are about 5 minutes left in the cooking time for the carrots and parsnips, make the brown butter. Place a non-stick skillet over medium-high heat. Add the butter and cook, stirring frequently, until the butter is foamy and flecked with little brown bits. This can take 2-3 minutes. Pour the brown butter into a large mixing bowl.
When the veggies are down cooking, add them to the bowl with the brown butter along with the chopped parsley. Toss to coat Season with more salt and pepper if needed. Serve warm with your favorite meals.
Notes
Cutting the veggies on the bias leaves more surface area touching the baking sheet to caramelize the natural sugars. If you prefer, you can slice them into coins (circles) instead.