Bring the vegetable broth, water, carrot trimmings, and dark green leek parts to a simmer in a large saucepan over medium-high heat. Reduce the heat to low, cover, and keep the broth hot while you prepare the risotto.

Melt half the butter in a Dutch oven over medium heat. Add the carrot pieces and a pinch of salt. Cook until the carrots are crisp-tender and starting to brown at the edges, about 8 to 10 minutes, then transfer them to a plate and set aside.

Add the remaining butter to the now-empty pot and melt over medium heat. Stir in the sliced leeks and cook until they are softened and translucent, about 5 minutes.

Add the rice to the pot and stir to coat the grains in butter. Cook until the edges of the rice grains are translucent but the centers are still opaque, about 3 minutes—toasting the rice this way prevents it from becoming mushy.

Pour in the wine and stir constantly until the liquid is fully absorbed by the rice.

Strain the hot broth into the rice mixture one ladleful at a time, stirring frequently. Wait for each addition to be absorbed before adding the next. Continue until the rice is tender but still has a slight bite in the center and the sauce is creamy.

Fold in the cooked carrots, chopped watercress, parmesan, and lemon juice. Stir gently until the watercress has just wilted and the cheese is melted. Season with salt and pepper to taste.

Serve immediately in warmed bowls while the risotto is still creamy and loose.