Place the halved new potatoes and baby carrots in a large Dutch oven or heavy-bottomed pot. Cover them with cold water by about 1 inch and add a generous pinch of salt.

Bring the water to a boil over medium-high heat. Once boiling, reduce the heat to a simmer and cook for 10 to 12 minutes, or until the potatoes and carrots are just starting to become tender when pierced with a fork.

Add the fresh green beans to the pot and continue to simmer for another 5 minutes. The beans should become bright green and slightly tender but still retain a bit of crispness.

Drain the vegetables carefully in a colander and immediately return them to the warm pot off the heat. Add the green peas, unsalted butter, heavy cream, whole milk, salt, and black pepper.

Return the pot to medium-low heat and gently stir the mixture until the butter is completely melted and the cream is steaming. Heat for 3 to 4 minutes, but do not let the mixture boil, or the dairy may separate.

Taste the broth and adjust the seasoning with additional salt and pepper if desired. Ladle the hot hodge podge into shallow bowls, garnish with fresh parsley, and serve immediately with warm crusty bread for dipping.