In a large soup pot, heat 1 tablespoon of the olive oil over medium-high heat. Add the diced onion and carrot and cook, stirring occasionally, until the vegetables soften slightly and get a nice coating from the oil — about 5 minutes. Add the garlic and celery and continue cooking for another 3-5 minutes, giving them a stir so everyone is happy together.
Add the flageolets and pour in water to cover — 4 to 5 cups. Then drop in the crushed red pepper, bay leaf and optional sage. Stir and let mixture come to a boil.
Reduce heat to low and let the beans simmer, with the pot lid on slightly ajar, to allow a little steam to escape and the bean broth to thicken slightly. Cook for about 90 minutes or until flageolets are tender.
Set aside to cool slightly. Fish out the red pepper, bay leaf and sage, then puree the beans using an immersion blender or food processor for a minute or two, until the mixture is uniform. Blitz until quite creamy or leave it a little chunky, depending on person-al preference.
Add with thyme leaves, balsamic vinegar and remaining tablespoon of olive oil. Process briefly again to combine. Season generously with sea salt and freshly ground pepper to taste.