Film the bottom of a deep pot (minimum 3 quart) with olive oil. Heat gently.
Cut the bacon into 2 inch slips and lay into warm pot, cooking until floppy, just barely crisping the edges. Remove and drain, reserving drippings in the pot.
Turn up your heat slightly and add chopped onion, cooking until glassy. Add garlic and cook, stirring, until garlic is faint brown and onion has begun to brown.
Deglaze with ¼ - ½ cup vermouth, stirring to reduce slightly.
Add squash, stock, reserved bacon, parmesan rind and bouquet garni. Cover and simmer for 30 minutes, venting slightly.
When the squash is soft enough to mash with a spoon, remove the pot from the heat, remove the bouquet garni and parmesan rind (wrap and refrigerate the rind for another use), add grated parmesan and, preferably using an immersion blender, purée until smooth. If you do not have an immersion blender, ladle batches into a stand blender or food mill and purée smooth, returning to pot when finished.
The fats will emulsify with the starch from the squash and simmering reduces liquid volume by about 20%, which combine to produce a satisfyingly thick soup. You’ll thin it slightly with a final treatment of fresh lemon juice, but if the soup is still too thick, fold stock or water a tablespoon at a time over low heat to reach desired consistency (don’t reboil or you’ll lose the fresh acidity of the lemon). Season to taste, portion and drizzle with EVOO just prior to serving.
We recommend bringing this to table with a selection of brined olives, bread sticks (or ciabatta), soft cheeses and a stony dry white wine (such as Vermentino).
If you’re figuring out what to do with the inevitable end-of-season bumper crop of squash, this recipe freezes very well - just hold off on the addition of the last dosing of lemon juice and EVOO.