Prepare the sweet potatoes: Peel and cut the sweet potatoes into roughly 1–2-inch chunks for even cooking.
Cook the sweet potatoes: Place them in a pot, cover with cold water, add a pinch of salt, and bring to a boil. Simmer until fork-tender, about 12–15 minutes.
Drain and mash: Drain the potatoes well, return to the warm pot, add butter and milk or cream, and mash until smooth. Stir in ground cinnamon if using, taste, and adjust salt. Keep warm.
Make the green sauce: In a blender or food processor, combine parsley, cilantro, basil (if using), garlic, capers, and red wine vinegar or lemon juice. Pulse to combine, then stream in the olive oil until you get a bright, slightly loose sauce. Season with salt, pepper, and red pepper flakes to taste. Taste and adjust acidity or salt as needed.
Bring the steak to room temperature: Pat steaks dry with paper towels, then season both sides generously with kosher salt and freshly ground black pepper. Let rest 20–30 minutes if you have time.
Heat the pan: Preheat a heavy skillet (cast iron preferred) over medium-high heat until very hot. Add 1–2 tablespoons of olive oil and let it shimmer.
Sear the steaks: Place the steaks in the hot skillet without crowding. For medium-rare, cook about 3–4 minutes per side depending on thickness; adjust time for your preferred doneness. Resist the urge to move the steak while it develops a brown crust.
Rest the steaks: Transfer steaks to a cutting board and tent loosely with foil. Let rest 5–8 minutes to allow juices to redistribute.
Finish the plates: Spoon a generous amount of mashed sweet potatoes onto each plate, slice the steak against the grain and place atop or beside the potatoes, then drizzle the green sauce over the steak (or serve on the side). Garnish with a few extra herbs or a lemon wedge if desired.