This is the recipe I've been making for years, adapted from Saveur. You'll need to soak the chickpeas overnight before blending in a food processor. You can form the patties in advance and bake (or fry) before serving.
Combine all the ingredients in a food processor and pulse, scraping down the bowl, a few times until evenly ground but not smooth.
Use a 1/4-cup measuring cup to portion the falafel mixture into slider-sized patties. Arrange on a baking sheet lined with parchment paper. (This step can be done in advance.)
Preheat the oven to 425 degrees F. Place a rimmed sheet pan in the oven for 5 minutes. Then, add the oil and heat for 1 minute.
Carefully arrange the falafel on the sheet pan about 2 inches apart. Bake until the bottom sides are golden brown, about 6 minutes. Flip the patties so that they land in oil and cook until the bottoms are golden brown and the falafel are heated through, about 5 minutes more.
To fry falafel, I pan fry instead of deep frying. Heat 1 1/2 inches of vegetable oil in a saute pan over medium-high heat until a few crumbs of the mixture sprinkled into the oil bubble. Cook the patties in batches to avoid overcrowding the pan for 3-4 minutes per side until deeply golden brown.