I bring a large pot of water to a rolling boil, then drop in the potatoes and let them cook for 10 minutes. After that, I add the corn pieces and chorizo and let everything boil together for another 5 minutes. Once the potatoes are fork-tender, I drain the whole pot and let it cool just enough to handle.
Once the boiled ingredients have cooled slightly, I start threading the potatoes, corn, sausage, and raw shrimp onto twelve long skewers, alternating pieces so every bite gets a mix. I lay the finished skewers on a baking sheet so they're ready to grab the moment my grill is hot.
While the grill heats up, I melt the butter in a small pan over medium heat with the paprika, chili powder, oregano, sea salt, minced garlic, and lemon juice. Once it's fully melted and fragrant, I pour half into a bowl for basting and keep the rest warm for serving on the side.
I oil my grill grates well and preheat to medium-high before basting the skewers with the reserved butter. They only need about 10 minutes on the grill, turning halfway through and basting once more so the shrimp turn opaque and everything gets a light char.
I like to pull the skewers off the grill right when the shrimp curl and turn pink, then serve them immediately with lemon wedges and the warm reserved butter on the side for dipping. Waiting too long lets the shrimp cool and firm up more than I like.