Season the pork. Lightly coat the entire pork roast with 1 teaspoon of olive oil.
Combine the paprika, thyme, garlic powder, onion powder, cayenne pepper, black pepper, and salt in a small bowl. Distribute the seasoning blend evenly over the pork, pressing it firmly onto all sides so the spices adhere to the surface.
Sear the roast. Warm 1 tablespoon of olive oil in a large skillet over medium heat.
Place the seasoned pork in the hot skillet and brown it thoroughly on every side until the exterior develops a deep golden color. Monitor the heat carefully to prevent the spice coating from scorching.
Transfer the browned pork directly to the slow cooker.
Make the honey butter sauce. Carefully wipe the skillet clean with a paper towel, then return it to medium heat.
Add the unsalted butter and allow it to melt. Stir in the freshly minced garlic and cook for approximately 1 minute, just until the garlic becomes lightly golden.
Add the honey, apple cider vinegar, salt, and black pepper. Stir thoroughly and allow the sauce to simmer vigorously for about 30 seconds.
Slow-cook the pork. Pour the prepared honey butter mixture over the pork in the slow cooker, then cover with the lid.
For pork loin, cook on LOW for 4–5 hours. For pork shoulder, cook on LOW for approximately 10 hours. Cooking time may require adjustment according to the exact size of the roast.
Rest the cooked pork. Remove the pork from the slow cooker and transfer it to a serving platter.
Loosely tent the roast with foil and allow it to rest for 10–20 minutes before slicing.
Prepare the finishing sauce. While the pork rests, transfer all of the liquid and cooking juices from the slow cooker to a large saucepan.
Stir the cornstarch together with an equal amount of cold water until smooth, then whisk this slurry into the cooking liquid.
Reduce and serve. Bring the sauce to a simmer over medium-high heat and cook for approximately 5 minutes, or until it reduces and develops a thick, syrup-like consistency.
Cut the rested pork into substantial slices measuring roughly 1.5–2 cm (⅗–⅘ inch) thick. Arrange on a serving platter and generously spoon the warm honey butter sauce over the pork.