Season the steak on both sides with salt and pepper. Let it sit at room temperature for 10 minutes while you start the sweet potatoes.
Place the cubed sweet potatoes in a pot and cover with cold water. Add a pinch of salt, bring to a boil, then reduce to a simmer and cook until very tender, about 12–15 minutes.
While the potatoes simmer, make the green sauce. In a food processor or blender combine parsley, cilantro (if using), garlic, capers, red wine vinegar or lemon juice, and red pepper flakes. Pulse to blend.
With the processor running, slowly drizzle in the olive oil until the sauce is emulsified. Taste and season with a pinch of salt and more acidity if needed. Set aside.
Drain the sweet potatoes well and return them to the pot. Mash with butter and milk or cream until smooth and creamy. Season with salt and pepper to taste. Keep warm.
Heat a heavy skillet or cast-iron pan over medium-high heat until hot. Add olive oil and swirl to coat.
Add the steak to the pan and sear without moving for 3–4 minutes to develop a good crust. Flip and cook another 3–4 minutes for medium-rare, or longer to desired doneness.
Transfer the steak to a cutting board and let it rest for 5–7 minutes. This helps the juices redistribute.
Slice the steak thinly against the grain. Spoon a generous amount of green sauce over the slices and serve with a scoop of mashed sweet potatoes on the side.