In a large pot, combine 8 cups low-sodium chicken or vegetable broth, 1 medium carrot (cut into chunks), 1 small quartered onion, 2 smashed garlic cloves (if using), 2 thin slices fresh ginger, 1 bay leaf, 1/2 teaspoon fine sea salt, 1/4 teaspoon whole black peppercorns, and 1 teaspoon apple cider vinegar if using. Stir gently.

Bring the pot just to a simmer over medium-high heat, then reduce to low so you see only small bubbles. Simmer uncovered for 30–40 minutes, topping up with a little water or broth if the liquid reduces too much.

Set a fine-mesh strainer over a large bowl or clean pot. Carefully pour the broth through the strainer, discarding the carrot, onion, garlic, ginger, bay leaf, and peppercorns. Taste and adjust salt, and add a squeeze of fresh lemon juice just before serving if desired. Serve warm in a mug or bowl, making sure no solids remain if you need a strict clear liquid.

In a medium pot over medium heat, warm 1 tablespoon olive oil or butter. Add the diced onion and cook for 3–4 minutes, stirring, until softened and translucent.

Stir in the sliced carrots and cubed Yukon Gold potato. Cook for 2–3 minutes, stirring so the vegetables do not stick, to build flavor.

Pour in 3 cups low-sodium broth. Add 1/2 teaspoon fine sea salt, 1/4 teaspoon ground turmeric, and 1/8 teaspoon white or black pepper if using. Bring the mixture to a gentle boil, then reduce heat to maintain a simmer.

Simmer the soup for 15–20 minutes, or until the carrots and potatoes are very soft and almost falling apart. The softer they are, the smoother the blended soup will be.

Turn off the heat. Carefully transfer the hot soup to a blender in batches, or use an immersion blender in the pot. Blend until completely smooth with no visible chunks. If needed, strain for an ultra-smooth full liquid texture.

Return the smooth soup to the pot if needed. Stir in 1/2–1 cup milk, half-and-half, or unsweetened plant milk until you reach your preferred thickness. If desired, add 2 tablespoons plain Greek yogurt and 1–2 teaspoons nutritional yeast. Warm gently on low until heated through without boiling.

Taste the soup and adjust with additional salt or a splash more milk or broth if it’s too thick. For a full liquid diet, the soup should be smooth and easily sippable or spoonable without chewing.

To a blender, add 3/4–1 cup unsweetened almond milk or dairy milk, 1/2 cup plain Greek yogurt, 1 scoop vanilla protein powder, 1 cup frozen strawberries, 1/2 medium banana, 1–2 teaspoons honey or maple syrup if using, and 1/2–1 cup ice as needed.

Blend on low, then increase to high until completely smooth and creamy. If it is too thick, add more milk; if too thin, add a bit more ice or frozen fruit. Taste and adjust sweetness lightly, especially if you are aiming for a lower-calorie shake. Serve immediately in a glass or insulated tumbler.