Heat olive oil over medium-high heat in a large pot. Add butter; allow butter to melt. Add onion, celery, and carrot and cook and stir until onion begins to turn translucent and golden, about 7 minutes. Stir in garlic; cook 1 more minute. Add beans and broth. Season with salt, pepper, rosemary, thyme, and cayenne pepper. Set heat to medium high and bring to a simmer. Reduce heat to low and let simmer until vegetables are tender, about 30 minutes.
Place bread cubes in a saute pan. Drizzle with olive oil; season with a pinch of salt and pepper. Toast bread cubes over medium heat until golden brown and crunchy, tossing occasionally, about 10 minutes. Sprinkle grated cheese over the bread cubes and continue to brown cubes about 2 more minutes.
Puree soup with an immersion blender until it is very smooth. Whisk in creme fraiche. Stir in lemon juice. Serve topped with browned bread cubes and chopped parsley.
