Crush garlic with rosemary, salt, and pepper to make a paste. Pierce meat with a sharp knife in several places and press the garlic paste into openings. Rub meat with remaining garlic mixture and 2 tablespoons olive oil.
Place the pork loin into a roasting pan and cook in preheated oven for 45 minutes, basting with pan juices several times.
Add the carrots, potatoes, and fennel to the pan and drizzle with 2 tablespoons olive oil. Season with more salt and pepper. Continue to roast until pork is no longer pink in the center, about 1 1/2 hours. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C).
Remove roast and vegetables to platter.
Pour wine into pan, and bring to a boil while scraping browned bits of food off bottom of pan with wooden spoon.