Fill a bowl with ice water and set it aside.
Bring 4 to 5 cups of water to boil in a large saucepan. Add the fava beans to the boiling water and cook for 2 to 3 minutes. Turn off the heat.
Using a skimmer or a slotted spoon, transfer the fava beans to the bowl with the ice water. The ice water will stop the fava beans form cooking further. Let the beans sit for about 5 minutes before draining.
Remove the outer skin of every bean. You end up with about 1 1/4 cups of beans.
Add the beans and the rest of the ingredients for the dip into a food processor. Blend until smooth, scraping down the sides of the bowl if necessary. Taste the dip and add more salt if you like. Transfer the dip to a bowl.
To make the pinwheels, spread 1/4 to 1/3 cup of the dip over a lavash wrap or tortilla. Make sure that the edge of the wrap facing away from you has a good amount of dip on it. The dip will help you seal the wrap once it's rolled up.
Sprinkle some chopped mint over the wrap. Next, cover with a layer of baby spinach. Line the carrots and pepper along the edge closest to you. Roll up the wrap. Slice into 1 1/2-inch slices and transfer pinwheels to a plate. Repeat for the remaining wraps.
Serve immediately.