Heat 3 tbsp of the olive oil in a 30 cm / 12-inch deep skillet over medium heat. Add the onion and 1/2 tsp salt, and cook for 6 to 7 minutes, stirring now and then, until soft and translucent but not browned.
Lower the heat to medium-low. Add the garlic, oregano, red pepper flakes, and tomato paste, and stir for 1 minute until fragrant. If the garlic turns brown it will taste bitter, so pull the pan off the heat for a few seconds if it's cooking too fast.
Add the beans, broth, and lemon zest. Bring to a gentle simmer and cook uncovered for 10 to 12 minutes. After about 5 minutes, mash roughly a quarter of the beans against the side of the pan with the back of a spoon. It's ready when the liquid has thickened and a spoon dragged across the bottom leaves a clear trail for a second.
Stir in the spinach and cook for 1 to 2 minutes until wilted. Take the pan off the heat, then add the lemon juice, parsley, black pepper, and the remaining 1 tbsp olive oil. Taste, and add more salt or lemon if needed.