Heat oil in medium skillet over medium-high heat. Add onions; cook until soft and translucent, about 7 minutes. Add garlic, paprika and pepper flakes; cook until fragrant, about 30 seconds more. Add tomato sauce to skillet, bring mixture to a boil; remove from heat and let cool 5 minutes.
In medium bowl, stir together slightly cooled tomato sauce mixture and mayonnaise. Season with adobo; cover and set aside.
Meanwhile, heat oil in large, heavy skillet over medium-high heat until oil registers 350°F on deep-fry thermometer. Add potatoes to oil in a single layer. Cook, in 2 batches if needed, until golden brown and cooked through, stirring occasionally, about 15 minutes. Transfer potatoes to paper towel-lined plate to drain; season with adobo.
Transfer potatoes to serving dish. Toss with warm brava sauce; garnish with parsley.