If squash is very hard to cut, microwave whole squash 2–3 minutes to soften. Cut in half, scoop out seeds, then cut into 2–3 inch pieces. Leave peel on—it softens completely during cooking.

Heat oil in a large pot or Dutch oven over medium heat.

Add onion and cook, stirring occasionally, until softened, about 5 minutes.

Add garlic and ginger. Cook, stirring constantly, until fragrant, about 1 minute.

Add squash pieces (with peel on), broth, salt, pepper, and turmeric if using. Stir to combine.

Bring to a boil over high heat, then reduce heat to medium-low. Simmer uncovered until squash is very tender and easily pierced with a fork, 20–25 minutes.

Remove from heat. Use an immersion blender to blend soup directly in pot until completely smooth, 1–2 minutes. If using a regular blender, work in batches: fill blender only halfway, remove center cap from lid, cover opening with a folded towel, and start on low speed to prevent hot liquid from erupting. Blend until smooth and return to pot.

Stir in coconut milk (start with ½ cup, add more for richer soup) and lemon juice or vinegar.

Taste and adjust seasoning with additional salt, pepper, or acid as needed. Warm gently over low heat for 2–3 minutes before serving.