I am very excited to make my first petit fours using this recipe! However, I see that the recipe calls for 4 eggs but I do not see eggs used in th...

Yes, the eggs would be beaten in with the butter and sugar. Add them in one at a time, and continue beating until it is pale and smooth. You want the sugar to dissolve so that there isn't any graininess. The butter will mean your whites won't beat up like a meringue, instead it will form a thick, almost batter like consistency when it is beaten enough. It will tend to fall from the beaters in a thick ribbon, which is a cue that it's beaten enough. Also take a judicious approach to the amount of almond flavoring you add. If yours is strong, it may not take the amount it calls for. Since it will be covered with almond paste as well, the flavor can overtake and overpower your fruit.