Sometimes the science of cooking works in strange ways.

In this case, it probably was the combination of slightly caramelized leeks and pureed starchy potatoes, though that’s just a guess. Whatever the cause, this easy soup tastes as though it contains about a pound of melted cheese — but it contains none.

That wasn’t the goal when crafting this recipe. The inspiration was a chilled potato and leek soup, something perfect for those still warm days of September. But as the prototype bubbled away, inspiration went in a new direction.

The chunks of potato were too large for a cold soup. And the thinly sliced leeks were too stringy. So the whole batch landed in the blender, where it was reduced to a thick, tan puree.

The result wasn’t the prettiest soup, but it was delicious in totally unexpected ways. Despite having just 11⁄2 cups of low-fat milk, it was utterly richly creamy and savory. It would be perfect accompanied by warm crusty bread.

The same basic approach to soups outlined in this recipe can be applied to any number of fall soups, including apple and butternut squash, potato and zucchini, and yellow onion and carrot.

In each case, substitute the different vegetables for those called for below, adjust the seasonings (though those listed work well for all of these combinations), and cook as directed. Batches that don’t include potatoes will cook in about half the time.

Each of these also is excellent topped with a bit of cooked bacon or pancetta.

Creamy Leek and Potato Soup

Start to finish: 30 minutes

Servings: 4

3 tablespoons olive oil

3 small leeks, ends trimmed, thinly sliced

1 teaspoon cumin

1 tablespoon grated fresh ginger

1 teaspoon smoked paprika

1 large apple, cored and diced

4 to 5 medium potatoes, cut into 1-inch chunks

2 to 3 cups vegetable or chicken broth

11⁄2 cups milk

Salt and freshly ground black pepper, to taste

Fresh chives, chopped (for garnish)

In a large saucepan, heat the olive oil over medium-high. Add the leeks and saute until limp, about 2 to 3 minutes. Add the cumin, ginger and paprika, then saute another minute.

Add the apple and potatoes and saute 1 minute. Add the broth (enough to cover half the potatoes) and milk, then bring to a simmer. Reduce heat to medium, cover and simmer until potatoes are tender, about 12 minutes.

Transfer the soup to a blender, in batches if necessary, and carefully blend until smooth. An immersion blender also can be used. Return the soup to the saucepan. Season to taste with salt and pepper.

If you prefer a thinner soup, more broth can be stirred in. To serve, garnish with chopped fresh chives.