First, heat vegetable oil in a large frying pan over medium-high heat. Once the oil is shimmering, add potatoes and season with paprika and salt. Cook until crispy, about 15 to 20 minutes, stirring occasionally. Once the potatoes are crisped on the outside, transfer them to a bowl and set aside.
In the meantime, grill the chorizo over medium-high heat until heated through and slightly charred, turning over once or twice during cooking. This should only take about 3 to 4 minutes per side.*
Transfer cooked chorizo to a cutting board and slice into quarter- to half-inch thick rounds.
Next, assemble the skewers. Add a slice of chorizo to a toothpick, followed by a potato cube, then another slice of chorizo. Alternatively, use two potatoes and one slice of chorizo between them - whichever you prefer!
Finally, plate the tapas skewers. Spread a spoonful of roasted garlic aioli on a serving dish, then plate the skewers on top of the aioli. Sprinkle with additional smoked paprika, then serve immediately.