Add the oil to a 12" skillet or large saucepan over medium heat.
Once hot, add the shallots and ⅛ tsp. salt. Stir occasionally until the shallots are soft and translucent, about 5 minutes.
Add the garlic, anchovy paste and red pepper flakes (if using) and stir for 30-60 seconds, until the garlic becomes golden and the paste has melted into the mixture. You can use the back of your spoon to mash the paste and spread it around.
Add the ground lamb. Break up the meat into smaller and smaller chunks as it browns.
As the lamb is browning, pour the can of whole peeled tomatoes and their juices into a bowl. Crush them by hand (careful, they squirt!) until they reach a chunky consistency. Add the balsamic vinegar to the empty can and swirl it around to pick up the last of the tomato juices and add it to the tomatoes.
Once brown, scoot the lamb away from the middle of the pan and add the tomato paste directly to the pan. Stir the paste for 30-60 seconds until it starts to darken.
Pour in the tomatoes and their juices, tomato sauce, dried mint and ⅛ tsp. salt and carefully stir through. Bring to a simmer and let it gently bubble for 5-10 minutes, until the sauce has slightly reduced and thickened to your liking. We're looking for a meat sauce with tomatoes here, not a tomato sauce with some meat in it. Taste and add salt, if necessary (I usually add another ⅛ tsp salt here).
Stir in 2 tablespoons of the fresh mint and a good grinding of black pepper. Serve the sauce with any of the recommended pairings, sprinkling the rest of the fresh mint over the top.