Preheat your oven to 400°F and line a baking sheet with parchment paper.
Place the cubed red beets on the baking sheet, drizzle with a tiny amount of oil, and roast for 25 minutes until tender and slightly caramelized.
Rub the beef tenderloin with 1 tsp olive oil, sea salt, black pepper, and dried thyme until evenly coated.
Heat a cast-iron skillet over medium-high heat and sear the beef for 2 minutes on each side to develop a golden crust.
Transfer the skillet to the oven and roast for 10 to 12 minutes, or until the internal temperature reaches 135°F for medium-rare.
In a small glass bowl, whisk together the extra virgin olive oil, lemon juice, and Dijon mustard to create the zesty dressing.
Remove the beef from the oven and allow it to rest for 8 minutes before slicing against the grain into thin strips.
Toss the arugula and roasted beets with the prepared dressing in a large bowl, then top with the sliced beef and fresh parsley.