In a large bowl, add the drained beans and mash them roughly with a fork. You want some texture, not a smooth purée.
Stir in the half-and-half (or milk), egg, and 2 tablespoons (30 ml / 1 fl oz) of melted butter or oil until thoroughly combined.
Gently fold in the all-purpose flour, salt, and pepper. Be mindful of how salty your beans already are.
Mix just until the flour is incorporated, being careful not to overmix. The batter should have the consistency of a thick pancake batter; add a splash more milk if it's too stiff.
Heat a non-stick skillet or griddle over medium-high heat (about 375°F / 190°C).
Add a little butter or oil to coat the surface.
Working in batches, spoon the batter onto the hot griddle to form 3 to 4-inch cakes.
Cook for about 4 minutes, or until bubbles begin to form on the surface and the edges look set.
Flip the griddlecakes and cook for another 3-4 minutes on the other side, until golden brown and cooked through.
Transfer the finished griddlecakes to a plate. You can keep them warm in a low oven (200°F / 95°C) while you cook the remaining batter.
Serve hot or at room temperature with your favorite toppings like sour cream, pesto, salsa, or a sprinkle of cheese.
Don't Over-Mash: For the best texture, mash the beans roughly with a fork. Leaving some partial beans intact adds a pleasant bite to the finished griddlecakes.
