Warm the olive oil in a large pot or Dutch oven, then cook the finely chopped onion until it begins to soften and take on light golden edges. The onion should smell sweet and mellow rather than sharp.
Add the garlic, celery, and carrots, then cook for about 10 minutes while stirring often. The vegetables should soften, smell sweeter, and show slight browning without letting the garlic darken.
Pour in the white wine and scrape the bottom of the pot as it cooks for about 5 minutes. Gentle steam will rise as most of the wine evaporates and the browned bits dissolve into the vegetables.
Stir in the cannellini beans, broth, tomato paste, salt, black pepper, red pepper flakes, Italian seasoning, bay leaves, dried thyme, and dried oregano. The tomato paste should disperse completely so the broth looks evenly seasoned.
Bring the soup to a boil, cover the pot, reduce the heat to low, and simmer for 15 minutes. Keep the liquid at a light bubble so the beans absorb the herbal flavor without breaking apart.
Remove the bay leaves, then carefully blend about 2 1/2 - 3 cups of the soup until smooth. The blended portion should look creamy and thick, with no visible bean pieces.
Return the puree to the pot and stir until it disappears into the broth, adding more broth if the soup feels thicker than you like. The finished base should coat a spoon lightly while still flowing easily around the beans.
Stir in the chopped kale and simmer for a few minutes, then taste and adjust the seasoning as desired. The kale should become tender while staying bright green, and a squeeze of lemon juice can lift the rich bean flavor.
Ladle the soup into bowls and serve while hot. The beans should be tender, the broth velvety, and the kale soft enough to eat easily.