Place the cubed potatoes in a large pot of cold, salted water and bring to a boil over medium-high heat. Simmer for 5-7 minutes until they are just fork-tender but still hold their shape, then drain well and pat completely dry with paper towels.

While the potatoes dry, heat 2 tablespoons of olive oil in a saucepan over medium heat. Add the finely diced onion and sauté for 4-5 minutes until softened and translucent.

Stir in the minced garlic, sweet smoked paprika, and hot smoked paprika, cooking for about 30 seconds until highly fragrant. Sprinkle the flour over the mixture and cook for 1 minute, stirring constantly to form a thick paste.

Gradually whisk in the crushed tomatoes, vegetable broth, and sherry vinegar. Reduce the heat to low and let the bravas sauce simmer for 10 minutes until it thickens into a rich, velvety consistency, then season with half of the sea salt.

In a large skillet, heat the remaining 1/4 cup of extra-virgin olive oil over medium-high heat. Carefully add the dried potato cubes in a single layer, working in batches if necessary so they do not steam.

Fry the potatoes for 8-10 minutes, turning occasionally, until they are deep golden brown and crispy on all sides. Transfer the crispy potatoes to a paper towel-lined plate and toss with the remaining sea salt.

To serve, arrange the warm, crispy potatoes on a platter and generously drizzle the smoky bravas sauce over the top. Serve immediately with toothpicks for an authentic Spanish tapas experience.