Preheat your oven to 500 degrees. Bring a large saucepot of water to a boil. Add the cubed potatoes to the boiling water, and simmer for 10 minutes.
Meanwhile make the aioli by mixing together one clove of the finely minced garlic with the mayonnaise, then set aside.
After the potatoes have boiled for 10 minutes, rinse and drain them very well. Toss the dry, par-cooked potatoes with 2 Tb olive oil and 1 tsp salt (or to taste). Spread the potatoes out evenly on a large parchment paper-lined baking sheet. Bake for 15 minutes, then carefully turn the potatoes over. Reduce the heat of your oven to 475 degrees and cook the potatoes 15-20 minutes longer, or until deeply golden brown and crispy.
Meanwhile, rinse the saucepot out and make the brava sauce in the same pot: Place the remaining 2 tsp olive oil, remaining clove of minced garlic, Mesa de Vida Smoky Latin Cooking & Seasoning Sauce, Sherry wine, 1/2 tsp salt (or to taste), and a pinch of cayenne pepper (if using) into the pan. Cook, stirring constantly, over medium heat until the sauce thickens just a bit, about 3-4 minutes. Set aside.
When the potatoes are golden brown and crispy, toss them with your brava sauce.
Place the potatoes into your serving dish. Drizzle with the garlicky aioli, or serve on the side for dipping.