Wash all vegetables thoroughly and cut the potatoes and carrots into uniform bite-sized pieces to ensure they cook evenly.

Place the potatoes and carrots in a large soup pot or Dutch oven and cover with just enough cold water to submerge them by an inch.

Bring the water to a boil over high heat, then reduce the heat to medium and simmer for about 10 minutes until the vegetables begin to soften.

Add the green beans, yellow wax beans, and fresh peas to the pot, continuing to simmer for another 8 to 10 minutes until all vegetables are tender but not mushy.

Carefully drain most of the water from the pot, reserving about 1 cup of the starchy cooking liquid in the bottom with the vegetables.

Reduce the heat to low and add the butter, heavy cream, and milk to the pot, stirring gently to combine without breaking the vegetables.

Allow the stew to heat through gently for 5 minutes, ensuring it does not come to a rolling boil which could curdle the dairy.

Season the dish generously with salt and freshly cracked black pepper, tasting the broth to ensure the flavors are balanced.

Ladle the hot Hodge Podge into bowls and garnish with chopped fresh chives before serving with a slice of crusty bread.