Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius) and line a large rimmed baking sheet with parchment paper.
In a large mixing bowl, combine the cubed beets, sweet potatoes, olive oil, dried thyme, salt, and black pepper.
Toss the vegetables until evenly coated with oil and seasonings.
Spread the vegetables in a single, even layer on the prepared baking sheet, ensuring they are not overcrowded to promote even browning.
Roast in the center rack of the oven for 40 to 45 minutes, tossing once halfway through the cooking duration, until the vegetables are fork-tender and slightly caramelized.
Remove from the oven and transfer the roasted vegetables to a serving platter.
Top immediately with crumbled feta cheese and chopped parsley.
Finish with a drizzle of balsamic glaze if desired and serve warm.