Preheat the oven to 325 degrees Fahrenheit. Pat dry 3 pounds pork shoulder and place it into a large roasting pan or Dutch oven.
Rub 1 tablespoon olive oil all over the pork shoulder.
In a small bowl, combine 2 teaspoons salt, 2 teaspoons pepper, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1 teaspoon paprika, and 2 teaspoons Italian seasoning. Rub the seasoning mixture evenly over all sides of the pork shoulder.
Arrange ½ white onion cut into large pieces, 4 carrots cut into large pieces, and 1½ pounds baby potatoes around the pork shoulder in the roasting pan.
Pour 2 cups chicken broth into the bottom of the roasting pan and sprinkle 2 teaspoons minced garlic over the vegetables and broth.
Cover the roasting pan tightly with a lid or aluminum foil and bake for 3½ to 4 hours until the pork is tender and easily pulls apart with a fork.
Remove the cover during the last 30 minutes of cooking to allow the pork and vegetables to brown slightly.
Let the pork shoulder rest for 10 minutes before slicing or shredding. Serve warm with the vegetables and pan juices.
Notes
Refrigerate the leftovers in an airtight container for up to 5 days.