For the compound butter: In a bowl, combine the softened butter with the sundried tomatoes, sage, parsley, Cajun spice, and salt. Whisk together until well blended. Transfer the mixture to a piece of parchment paper and roll into a cigar shape about 1 1/2 inches thick. Refrigerate until ready to use.
For the pork: Slice the loin into 3/4-inch thick slices, and then one by one, cover with plastic wrap and pound with a meat mallet until each slice is flat and even (about a 1/4-inch thick).
Season the flour with salt and pepper, and then dredge the pork in the seasoned flour.
Heat the oil in a heavy bottom saucepan over medium-high heat. Season the pork with salt and pepper. Once the oil has heated, add the floured pork to the pan and allow to cook until browned, 1 to 2 minutes. Reduce the heat, flip, add some thyme and parsley, and repeat the process on the second side until finished cooking, 2 to 3 minutes. Once cooked, remove from the pan and keep warm. Repeat the process until all the pork is cooked.
For the asparagus: Bring a pot of water to a boil and add salt. Trim the woody bottoms of the asparagus and peel the stalks. Blanch in the boiling water until bright green, 2 to 3 minutes. Remove from the water and season with salt and pepper.
Place asparagus in the center of a serving plate, arrange the pieces of cooked pork on top, and top with a 1/4-inch disk of sundried tomato butter. Garnish with parsley. Store the remaining butter wrapped in plastic in the refrigerator.