Heat the broth and garlic in a saucepan over medium heat until steaming; keep warm. Melt 2 tablespoons butter in a large Dutch oven or pot over medium-high heat. Add the leek and cook, stirring occasionally, until softened, 2 to 3 minutes. Add the rice; cook, stirring, until toasted, 2 to 3 minutes. Stir in the wine and cook, scraping up any browned bits, until absorbed, 3 to 5 minutes.
Add 3 cups hot broth to the rice; cook, stirring constantly, until mostly absorbed, 8 to 10 minutes. Add 3 more cups hot broth; continue cooking, stirring, until the risotto is tender and thickened, 12 to 14 minutes.
Reduce the heat to low and stir in the peas, ham, cheese and the remaining 2 tablespoons butter. Stir in more hot broth if the risotto is too thick; season with salt and pepper. Top each serving with mint, more cheese and the lemon zest.