Assemble your ingredients.
Place the potatoes in a large pot and cover them with cold water. Season the water with salt. Bring to a boil and cook the potatoes until they can be easily pierced with a sharp knife but still al dente. Drain in a colander and set aside.
While the potatoes are boiling, make the seasoning paste. In a small mixing bowl, combine 1 clove of minced garlic, paprika, oregano, cumin, vinegar, and salt. Mix this until it forms a paste.
In a large, heavy skillet (preferably cast-iron), heat 2 tablespoons of olive oil over medium-high heat. Add the tomatoes and jalapeños. Cook for 4 to 5 minutes until the tomatoes release their juices to make a sauce and the jalapeños are tender.
Add the remaining garlic and cook for an additional 30 seconds. Stir in the seasoning paste. Once warm, transfer everything to a bowl and wipe out the skillet.
Turn the heat down to medium. Add the rest of the olive oil to the skillet. Add the potatoes and season with salt and pepper. Cook until the potatoes begin to brown, stirring every 2 minutes. Continue until all the potatoes are golden brown and a little crispy.
Stir in the tomato and jalapeño mixture to coat the potatoes.
Transfer to a serving bowl and garnish with the cilantro leaves. Serve while hot with lemon wedges.