For the crema: Combine the yogurt, lime zest and juice, cilantro and adobo sauce in a small bowl, stirring well to combine. Season with salt and pepper and set aside.
For the quesadillas: Preheat a grill pan and spray with nonstick spray.
Soak the onions in the jalapeno juice about 10 minutes. Drain.
In a large bowl, mix together the jalapenos, onions, pork and cheese. Divide the mix on top of 2 tortilla rounds. Top each with another tortilla round. Spray the round with olive oil and place face down onto the grill. Grill until the cheese is melted and the tortillas begin to brown, about 3 minutes. Flip and cook an additional 3 minutes. Remove the quesadillas from the grill pan, cut each into quarters and serve with the crema.
Preheat the oven to 425 degrees F.
In a small bowl, mix the olive oil, garlic, salt, and pepper. Using a pastry brush, spread the mixture all over the pork shoulder.
Set the meat on a rack set into a roasting pan. Roast for 20 minutes, and then reduce the heat to 325 degrees F. Continue to cook until an instant-read thermometer inserted into the shoulder reads 185 degrees F, about 4 hours. Remove the pork from the oven and let stand until cool enough to handle, about 30 minutes.