Gently scrub the potatoes and cut them in half if they're large. Wash the carrots and slice them in half lengthwise. Trim the beans and cut them in half. Shell the peas.
Place the potatoes in a large pot and cover with about 5 litres (5 quarts) of cold water. Add 2 tablespoons of table salt to the water. Bring to a boil, then reduce the heat to a gentle-yet-lively simmer for 8 to 9 minutes, or until the potatoes start to soften.
Add the carrots and continue cooking for 5 to 7 minutes, or until both the potatoes and carrots are nearly tender.
Add the green and yellow beans and simmer for another 5 minutes, or until the beans are bright and just tender.
Stir in the peas and cook for 1 to 2 minutes, until they are bright green and just cooked.
Drain off most of the cooking water, leaving about 1 cup (250 ml) in the bottom of the pot to help form the cream broth.
Add the cream, butter, ¾ teaspoon salt, and black pepper. Return the pot to low heat and cook gently, stirring occasionally, until the butter melts and the vegetables are heated through, about 2 to 3 minutes. Taste and adjust the seasoning if needed. Serve hot.
Notes
Keep the water at a gentle simmer instead of a hard boil to avoid breaking up the tender vegetables.
Stir gently once the cream and butter are added. New vegetables are delicate and can easily fall apart.
Taste the broth at the end and adjust the salt and pepper until it tastes right to you.
Storage
Store leftovers in an airtight container in the fridge for up to 3 days. Reheat gently in a pot over low heat, stirring occasionally, until warmed through. Avoid boiling once the cream has been added, as it may split.
Freezing Hodge Podge is not recommended, as the cream can separate and the vegetables may become mushy.