Prepare the beans: Heat 1 tablespoon of olive oil in a large skillet over medium heat. When the olive oil is fragrant, add the garlic to the skillet and toss. Sauté the garlic for 1 minute, then add the butter beans to the pan and season them with salt. Toss to coat. Saute the beans for 3-4 minutes, then transfer them to a mixing bowl.
Add the lemon juice and pepper to the beans and toss. Set aside.
Prepare the tomato sauce: Heat 2 more tablespoons of olive oil in the same skillet. When the olive oil is fragrant, add the onion to the pan and season the onion with ¼ teaspoon of salt. Let the onions sauté for 10 minutes, stirring occasionally so they do not burn.
While the onions are sauteeing, puree the tomatoes in a food processor or blender until smooth.
After 10 minutes, add the garlic to the onions and saute for an additional minute. Then, add the tomato sauce, tomato paste, brown sugar, remaining salt, and red pepper flakes to the skillet. Stir all of the ingredients together until combined. Bring to a boil over high heat, then turn the heat to low, and let the sauce simmer for 15-20 minutes or until it reduces and becomes thick.
Prepare the gremolata: Add all of the ingredients for the gremolata into a bowl and stir to combine. Set aside for later.
Once the sauce has reduced and thickened, add the butter beans and stir. Let the beans simmer for 10 minutes, then remove them from the heat.
Toast the bread by heating butter or olive oil in a separate skillet and add the bread. Toast the bread on each side for 2-3 minutes or until golden brown (how long you toast the bread depends on your stove top, so be sure to keep an eye on the bread).
Remove the toast from the skillet and top with the bean mixture, parmesan cheese, gremolata, and a pinch of salt.