Pulse paprika, sugar, tomatoes, garlic, onion, salt, and white pepper in a small food processor until coarsely ground. Heat olive oil in a 2 -qt. saucepan over medium - high heat. Fry tomato mixture, stirring occasionally, until slightly reduced, about 5 minutes; set bravas sauce aside
Heat 2" olive oil in a 6-qt. saucepan until a deep -fry thermometer reads 220°. Add potatoes all at once to oil; cook until tender and pale golden, 35 –40 minutes. Using a slotted spoon, transfer potatoes to paper towels to drain; chill 30 minutes. Remove oil from heat.
Return pan of oil to heat until a deep -fry thermometer reads 350°. Working in batches, fry potatoes until golden brown and crisp, 4 –5 minutes. Using a slotted spoon, transfer potatoes to paper towels to drain; season with salt. Drizzle potatoes with the reserved bravas sauce and mayonnaise; garnish with parsley if you like.