Combine parsley, garlic, canola oil, salt, pepper, and lemon juice in a blender and purée to make the gremolata. In a container with a lid, coat the steak with gremolata. Cover and place in the refrigerator overnight or for at least 4 hours.
Preheat the oven to 375°F.
In a large pot, cover the potatoes with cold water and bring to a simmer. Simmer until soft but not mushy, about 16 to 20 minutes. Drain the cooked potatoes and return to the saucepan; place over a medium-low heat for 1 to 2 minutes to dry out the moisture, then mash using a potato masher. Quickly fold in the cream cheese, heavy cream, butter, sour cream and parmesan and season to taste.
On a baking sheet, toss the broccoli with the garlic, chile flakes, oil, salt and pepper. Roast for 12-15 minutes, until crisp tender.
Heat a grill or large skillet to medium-high. Remove the steaks from the marinade, discarding excess marinade and grill for 2 to 3 minutes per side to sear.
Transfer to a baking sheet and roast to desired doneness, 8 to 10 minutes (for medium, the internal temperature should be 135°F, 125°F for rare). Rest for 5 minutes before serving.
Add all of the salsa verde ingredients except the oil to a blender and purée until smooth. With the motor running, drizzle in the oil to emulsify. Season with salt and pepper.
To serve, divide the mashed potatoes between plates. Top with steak, roasted broccoli, and salsa verde. Sprinkle with grated parmesan.