Preheat oven to 350°F (180ºC). Line an 8-by-8-inch baking pan with parchment paper and set aside.
In a small skillet, melt butter over medium heat. Continue cooking butter 3–5 minutes or until browned with a very nutty fragrance.
In the bowl of a food processor, puree chickpeas on high speed until almost smooth, stopping to scrape the sides of bowl as needed.
Add browned butter and vanilla; process until smooth.
Add eggs; pulse 3–4 times to combine.
Add sugar, flour, baking soda and salt; pulse 4–5 times to combine.
Add pecans; pulse once or twice just to combine.
Spoon batter into prepared pan.
Bake for 28–30 minutes or until a wooden toothpick inserted in the center comes out clean.
Cool in pan on a wire rack.
