Heat the olive oil in a large Dutch oven over medium-high heat. Season the lamb chunks with kosher salt and black pepper, then sear them in batches until browned on all sides. Transfer the browned lamb to a plate.
In the same pot, add the chopped onion and sliced carrots. Sauté for about 5 minutes until they begin to soften. Stir in the minced garlic and cook for an additional minute until fragrant.
Pour in the red wine to deglaze the pot, carefully scraping up any browned bits from the bottom. Let the wine reduce slightly for 2 minutes.
Return the seared lamb to the pot. Add the broth and halved new potatoes. Bring the stew to a boil, then immediately reduce the heat to low, cover, and simmer for 1.5 to 2 hours, or until the lamb is perfectly tender.
During the last 5 minutes of cooking, stir in the spring peas to gently warm them through and maintain their vibrant green color.
Remove the stew from the heat and stir in the freshly chopped mint leaves right before serving to create the bright, minted broth.