Preheat the oven to 350 degrees F. Place the potatoes on a rack in the oven and set a timer for 30 minutes.
Pick the parsley and oregano leaves and roughly chop; set aside.
Gather all the peppers, the shallot and tomatoes and julienne thinly. Thinly slice the garlic and place with the pepper mixture.
Pour the oil into a saute pan and place on medium heat. Add the pepper mixture, smoked paprika, 1 teaspoon salt and 1/2 teaspoon black pepper. Saute for 3 to 4 minutes, then reduce the heat to low and cook for 3 more minutes. Set the piperade aside.
Small dice the onion and place in a medium bowl.
The potatoes should be ready. Holding them in a towel, you can easily peel them with a knife. Shred the hot potatoes on a box grater and mix with the onion.
Add half of the melted butter to a 12-inch skillet on low heat. Press the potato mixture into the skillet and sprinkle with 3/4 teaspoon salt; let cook until crisp underneath, 6 to 7 minutes. Flip and repeat with the remaining melted butter and another 3/4 teaspoon salt.
Dump the potato cake onto a cutting board and cut into sixths.
Gently fold the chopped parsley and oregano into the piperade.
To serve, place a portion of the potato cake on a plate and top with piperade. Garnish with a few whole parsley leaves.