Build the Aromatic Foundation: Preheat your oven to 400°F (200°C) with a rack in the center. In a large, oven-safe skillet, heat the olive oil over medium heat. Add the onion, carrots, celery, and red bell pepper. Cook, stirring occasionally, for 8-10 minutes until the vegetables are thoroughly softened and sweet.
Activate the Flavors: Add the minced garlic, smoked paprika, oregano, red pepper flakes, black pepper, and cinnamon to the skillet. Stir constantly for 60 seconds until the spices are deeply fragrant.
Infuse the Tomato Base: Pour in the crushed tomatoes and low-sodium vegetable broth. Stir everything together, scraping up any flavorful bits from the bottom of the pan. Bring the sauce to a gentle simmer.
Integrate the Beans and Herbs: Stir in the rinsed butter beans, half of the chopped parsley (1/4 cup), and all the fresh thyme. Continue to simmer on the stovetop for 5 minutes to allow the beans to absorb the flavors of the sauce.
Transform in the Oven: Smooth the top of the bean mixture with a spatula. Carefully transfer the skillet to the preheated oven. Bake, uncovered, for 15-20 minutes, or until the sauce has thickened and the top is slightly browned.
Brighten and Serve: Remove the skillet from the oven. Stir in the fresh lemon juice to brighten the flavors. Garnish with the remaining fresh parsley, a light sprinkle of the crumbled feta, and a final, generous drizzle of high-quality extra-virgin olive oil. Serve hot.