Mix together the butter, sugar and salt in a large cast-iron pot with a candy thermometer attached over medium heat. Stir until the butter is melted and comes to a boil. Cook until the temperature reaches 285 degrees F and the mixture turns an amber color. Stir occasionally.
Meanwhile, toast the almonds in a large skillet over medium heat until they turn golden brown and you can smell the almond oils, stirring for even toasting, 7 to 10 minutes. Drop on a parchment-lined baking sheet and sprinkle with flaked sea salt.
Dig the sticks into the apples. Grab an apple by the stick with one hand and with a silicone spatula in the other hand rub the toffee all around the lower half of the apple. Roll the apple in toasted almonds, and then repeat with the remaining apples. Stand on the sides of the baking sheet to cool. Place the caramel apples on a serving platter.