Preheat the oven to 425°F. Thinly slice one lemon half into rounds. Juice the remaining lemon half. Add lemon rounds and fennel wedges to a baking sheet, and gently toss with just 1 tbsp olive oil, salt, and pepper. Roast until lemon is slightly browned and fennel is soft, 18 to 20 minutes.

Drain and rinse cannellini beans. Combine lemon juice, just 1 tbsp olive oil, garlic, shallot, red wine vinegar, parsley, and salt and pepper in a medium bowl. Add the beans and toss to coat.

Divide roasted fennel wedges between two plates. Spoon marinated beans on top. Garnish with crispy lemon rounds and sprinkle with Aleppo or red pepper flakes.