Combine paprika, cayenne, sugar, tomatoes, garlic, salt, and pepper in a food processor. Pulse until coarsely ground.
Heat olive oil in a medium saucepan over medium-high heat. Add the tomato mixture, stirring frequently, until the sauce is hot and slightly reduced, about 5 minutes. Set aside.
Fill a large heavy saucepan (I use my Dutch oven for this) with 2-inches of canola oil and heat over medium-high heat. Once the oil reaches 220 degrees F, add potatoes all at once to the oil. Cook for 35 to 40 minutes, stirring occasionally to make sure they don't stick to the bottom. Use a slotted spoon to remove the potatoes to paper towels to drain.
While the potatoes are cooling, return the oil to the heat and increase temperature of the oil to 350 degrees F. Fry the potatoes in batches, making sure not to overcrowd the pan, until golden brown. This will take approximately 4 to 5 minutes per batch. Remove to a new set of paper towels to drain. Sprinkle with salt.
Add potatoes to serving dish and top with the tomato sauce. Serve warm, with a garnish of freshly chopped parsley.