Heat 1 1/2 tbsp olive oil in a medium skillet on medium-high heat. Add shallots and cook until softened, about 2–3 minutes. Add white beans, nutmeg and salt & pepper to taste, and continue to cook for 5–8 minutes until beans soften.
Transfer bean mixture to a mini-food processor, add juice of 1 lime, and pulse until it forms a puree.
Build the quesadillas: starting with one tortilla, spread 1/4 of the bean mixture on top. Add a handful of baby spinach, and top with cheese. Top with another tortilla. Repeat to build four.
Heat a medium skillet over medium-high heat. Add a teaspoon of olive oil—when heated and shimmering, add one quesadilla. Cook until the tortilla crisps up and the filling starts to melt, then flip. Cook until the bottom is golden and the filling is nice and melty.
Slice and serve!