Add parsley, garlic, lemon juice, ¾ cup olive oil and ¾ tsp salt to a food processor and pulse about 20 times.
Place skirt steak in a container or bowl and cover with ½ cup of the marinade. Let sit for 1 hour.
While the skirt steak marinades, bring a medium pot of salted water to boil. Once the water is boiling, add the potatoes. Cook for 3 to 4 minutes or until the potatoes are fork tender. Strain and place in a medium sized bowl. Coat potatoes with 1 tbsp olive oil and ½ tsp salt.
Preheat grill to high. Grill the skirt steak for 2 minutes on each side then remove from heat and let rest for 5 minutes.
While the steak rests, place the potatoes in a large grill basket cook right on the grill until golden brown, about 6-8 minutes. Flip ½ way in between.
Use a sharp knife to cut the steak against the grain. Plate with potatoes and drizzle the remaining gemolata over the steak and potatoes.