Preheat oven to 350 degrees F (175 degrees C). Arrange squash, cut-side up, on a baking sheet.
Bake in the preheated oven until squash is tender, 30 to 40 minutes; cool slightly. Remove skin from squash and chop the flesh.
Heat canola oil in a large pot over medium heat; cook and stir onion and white parts of leek until golden brown, 10 to 15 minutes.
Mix water, green parts of leeks, potatoes, baked squash, and carrots to onion mixture; bring to a boil. Reduce heat, cover pot, and simmer, stirring every 10 minutes and adding more water as needed, until vegetables are tender, about 1 hour.
Pour vegetable stock into vegetable mixture; season with garlic salt and pepper. Raise temperature to medium and cook until boiling, 15 to 20 minutes.
