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, cover the steak with gremolata to marinate. Cover and place in the refrigerator for 4 to 24 hours.
For the onions, heat the red wine in a saucepan until the liquid reduces by half. In a large skillet, heat the butter on high heat until it begins to brown. Add the onions, salt, and sugar until the onions begin to caramelize. Add the garlic and cook for another 5 minutes. Add the vinegar and cook for 5 more minutes. Add the reduced wine and thyme, lower the heat and simmer for 25 minutes. Combine the cornstarch and water and stir into the onions. Cook, stirring for another five minutes, until thickened. Remove from the stove and set aside.
Preheat the oven to 400℉. Toss the potatoes with melted duck fat, salt, and pepper on a baking sheet. Spread into a single layer and bake for 20 minutes, until crisp. Top with chopped parsley.
Heat a grill or large skillet to medium-high.
Remove the steaks from the marinade, discarding 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-rare the internal temperature should be 135°F, 125°F for rare). Rest for 5 minutes before serving.
Bring a large pot of salted water to a boil for the green beans. Prepare an ice bath by filling a large bowl with water and ice. When the water boils, add the green beans for 2-4 minutes then immediately put them into the ice bath to stop cooking. Take them out of the ice bath after 1-2 minutes.
Let the steak rest for 3-5 minutes before serving and plate with a side of green beans and roasted duck fat potatoes, topped with red wine braised onions.