First, cook your vegetables. Bring a large pot of salted water to boil. Par-cook carrots and potatoes for five minutes until carrots and potatoes are fork tender, then blanch the peas and beans for about a minute in the same pot. Strain vegetables and set aside. In a heavy-bottomed pot or Dutch oven, melt butter over medium heat, add vegetables, and cook to warm through. Add milk and cream and bring the soup to a boil. Turn the heat down to low and season with salt and pepper. Add dill and chives and let simmer for at least 10 minutes. Serve warm.