First off: feel free to use a larger cut of pork. All you will need to do is adjust your cooking time. The marinade will aptly cover up to 5-6 lbs. :) Okay here we go!!

I recommend prepping a day before so that the pork can sit over night in the marinade. However 2 hours is adequate

Take a large bowl and mix together mustards, garlic and balsamic vinegar. Take 2 of the 4 sprigs of rosemary and chop finely. Add to mixture. Pour contents into gallon size ziploc bag. Rinse off pork under water and pat dry. Coat liberally with salt and pepper then place in bag. "Shake" the bag to coat well in marinade and place in fridge. Again, over night is best but 2 hours is sufficient.

Preheat oven to 325°F. Take pork out of bag, wipe off excess mixture into a bowl and sear in skillet ( i used a cast iron) on medium high heat for 2 minutes on each side. In a 13x9 inch glass dish, place one rosemary sprig in the middle, then place pork in on top of sprig, fat side up. Pour contents of ziploc bag into bowl and add olive oil. Using a whisk, stir briskly until emulsified. Using a pastry brush, brush mixture over pork liberally. Cut butter into 1 tbsp divisions and dot over pork, leaving some to line the dish bottom. Cut remaining rosemary sprig into eigths and also dot pork and dish bottom.

Take prepped carrots and apples in a large bowl toss well with salt, pepper and remaining olive oil. Set aside.

Cook pork 45 minutes per pound. Add carrots and apples to dish 45 before completing.