Add diced potatoes to a large bowl and cover with cold water. Let sit for 40-60 minutes, then drain and rinse thoroughly (this removes excess starch for super crispy potatoes). Pat the potatoes dry with a clean towel.
Whisk together olive oil, tomato paste, and lemon juice. Stir in cornstarch, salt, smoked paprika, oregano, garlic powder, cumin, and cayenne.
Pour the spice mixture over the potatoes and toss well to coat.
Spread potatoes onto parchment paper-lined baking sheet and roast for 35-45 minutes, stirring 2-3 times throughout, until potatoes are crispy.