Preheat the oven to 400F. Brush the bottom of a 10-inch cast iron skillet or a baking dish with oil.

Heat the 1 tablespoon oil in another large skillet over medium-high heat. Add the ground beef and cook, stirring to break up the meat, until it begins to brown, about 5 minutes. Add the onion, garlic, and salt and continue cooking until the vegetables have softened but not browned, 5 to 8 minutes more. Add the coffee and cardamom and stir to combine. Add a splash of water and scrape the bottom of the pan to deglaze it. Set aside to cool down.

Soak the matzo in warm water until pliable, about 1 minute. Gently place each soaked matzah between two tea towels and press to absorb any excess moisture. Line the bottom of the oiled cast iron skillet with the matzo, breaking up the pieces as needed to completely cover the bottom and sides of the skillet. Spoon the beef mixture over the bottom and cover the top with more matzo, pressing at the edges to seal. Brush with the beaten egg and bake until the mina is golden brown and crisp, about 30 minutes. Let stand for 5 minutes.

Invert the mina onto a serving platter. Slice into wedges and serve topped with the charoset.