In a medium bowl, mix together the masa, salt, and warm water. Cover the bowl with plastic wrap and allow the dough to rest for 10 minutes.
Add the refried beans to a bowl of a food processor and pulse until the beans become a paste. Alternatively, you could mash them with a fork.
Separate the dough into 4 balls. Roll each ball into an oval shape. Using for thumb, make a long, deep well in the center. It will resemble the shape of a cigar. Place 1 scant teaspoon of the beans into the well. Pinch the cavity closed, enclosing the beans completely.
One at a time place each piece of filled dough between two pieces of plastic wrap, Using a rolling pin, lightly press into a 4-inch-long oval that is ¼-inch thick.
Preheat your skillet over medium-high heat and brush with ½ teaspoon of vegetable oil. Add the huaraches and cook for 1 to 2 minutes on each side, flipping when lightly golden brown. Continue until all 4 huaches are cooked. Remove from skillet and set aside.
Place the skillet over medium-high heat, and pour in vegetable oil until it reaches ½ inch up the sides. Once the oil is hot, carefully add the huaraches to the pan and fry for 1 to 2 minutes, until golden brown on each side. Gently turn and cook on the opposite side for 1 to 2 minutes more. Transfer to paper towels to drain. Serve hot.