Halve the leeks lengthwise and slice them into thin half-moons. Rinse well in a colander to remove any grit. Chop the celery into small pieces.

Melt the butter in a 5-quart Dutch oven over medium-high heat. Add the leeks and celery, then stir to coat them in butter. Cover and cook for about 15 minutes, stirring often, until very soft. If the vegetables look as if they might brown, add 1/4 cup of water.

Core the pears, leave the skin on, and cut them into small chunks. Add them to the pot, stir, cover, and simmer for about 15 minutes, stirring occasionally, until soft and juicy.

Pour in the vegetable broth and bring the mixture to a boil. Lower the heat, cover the pot, and simmer for 20 minutes.

Let the soup cool for a few minutes. Blend it in batches, filling the blender no more than halfway. Vent the lid and hold it down with a towel. For a smooth finish, press each batch through a wire mesh sieve into a bowl with a spatula. Discard the leftover pulp.

Rinse the pot and return the strained soup to it. Bring the soup to a gentle simmer over low heat, then whisk in the heavy cream. Set aside a little Stilton for garnish. Crumble the rest and whisk it into the soup a bit at a time until melted and smooth.

Ladle the soup into bowls and top each serving with toasted walnuts and some of the reserved Stilton. Serve warm, ensuring not to let the soup boil after adding the cream and cheese.