In a large Dutch oven or heavy-bottomed pot, combine the baby potatoes, sliced carrots, vegetable broth, and kosher salt. Bring the mixture to a gentle boil over medium-high heat.

Once boiling, reduce the heat to medium-low, cover the pot tightly, and let it simmer for about 10 to 12 minutes. The potatoes and carrots should be just starting to become tender when pierced with a fork.

Add the green beans, yellow wax beans, and green peas to the pot, stirring gently to combine with the broth and root vegetables. Cover and continue to simmer for another 5 to 7 minutes until all the vegetables are tender but still vibrant in color.

Reduce the heat to low and stir in the unsalted butter and heavy cream. Allow the stew to gently simmer uncovered for 3 to 5 minutes, letting the creamy broth slightly thicken and beautifully coat the vegetables. Do not let it boil vigorously, or the cream may separate.

Remove the pot from the heat and stir in the freshly cracked black pepper and chopped parsley. Serve hot in shallow bowls with a thick slice of crusty bread to soak up the rich, buttery cream sauce.