If you like you can peel and cut the potatoes ahead of time and place in a plastic freezer bag with a tablespoon of lemon juice and the minced garlic. I will add the baby carrots and let them marinade as well. Place the bag in an ice chest until your get to the camp site and are ready to cook.
Rub the pork roast completely with dry rub and set aside. Add to Dutch Oven. You can use a #12 deep sided camp oven. A camp dutch oven has 3-4 legs on the bottom so you can place embers around under the dutch oven. It also has a rim around the lid to keep the coals from sliding off.
Create a wood fire burned to embers. Add a metal grill for the oven and pour 2-3 tablespoons of olive oil in the dutch oven. Allow the oil to heat up. Now place the roast into the hot oil and sear on all sides. This won't take more the a couple minutes on each side. When the pork roast is seared, pour 12-16 ounces of beef or chicken broth into the dutch oven. Add the two Granny Smith Apples (quartered) and two onions (quartered).
Cook the roast one hour, check the pork roast and turn it. Add more broth as needed. You want at least 2 inches of liquid in the bottom of the oven at all times. After one and a half hours, add the chopped potatoes, baby carrots and minced garlic. Add broth as needed.
After 2 hours of cooking, have a fork and meat thermometer handy to check for doneness of the potatoes and carrots. Use the meat thermometer to make sure the pork roast reaches at least 170 degrees. Always check the internal temperature of the roast away from the bone. I check several places.