To make the caramel apples:
Prepare a cookie sheet with a lightly buttered sheet of parchment, set aside.
Once the caramel reaches the right temperature, remove from the heat and allow it to cool to about 200 degrees F. It will begin to thicken as it cools. It should be thin enough to coat the apple, but thick enough to cling to the fruit.
While the caramel is cooling, stick the lollipop or popsicle sticks into the apple. Make sure they are deep enough that they won't fall out while you are dipping the apples in the caramel.
Dip the apples into the caramel. I like how they look when some of the apple is still showing, but you can completely cover them if you prefer. Hold the apple over the pot of caramel and allow some of the excess to drip off before placing them on the sheet of buttered parchment.
If you want, dip the bottom in the crushed peanuts.
Keep the apples in a cool, dry place and they will last for a few days, loosely covered with plastic.