Combine the first measures of sugar (4 tablespoons) and water (3 tablespoons) in a small saucepan. Gently stir together until it feels like wet sand. Do the same thing with the second measures of sugar (6 tablespoons) and water (3 tablespoons) in another small saucepan.
Place both saucepans on the stove and begin to heat them up. Heat the first saucepan (the one with 4 tablespoons sugar and 3 tablespoons water) over medium heat. Heat the second saucepan (the one with 6 tablespoons sugar and 3 tablespoons water) over medium low heat. Heat the first sugar water mixture to 115 degrees C (239 degrees F), keeping track of the temperature with an instant-read or candy thermometer.
While the sugar is heating up, whip the egg whites in a stand mixer fitted with the whisk attachment. Whip until soft peaks form. If the egg whites reach medium soft peaks before the first sugar hits 115 degrees C (239 degrees F), slow your mixer down and let the sugar catch up. Or, if you notice that the sugar is nearly at 115 degrees C (239 degrees F) and the egg whites are still a ways from becoming soft peaks, turn the heat way down under the first measurement of sugar water. Ideally, you want the egg whites to reach a soft peak at the same time the sugar water hits 115 degrees C (239 degrees F).
Once the first sugar measurement reaches this temperature, remove it from the heat and very carefully pour it into the egg whites while the mixer is on low.
When all of the sugar is successfully added to the egg whites, turn the mixer speed back up and turn the heat under the second sugar water mixture to medium. You know what this mixture of sugar water to reach 120 degrees C (248 degrees F). Once it reaches this temperature, remove it from the heat and very carefully pour it into the egg white mixture. Let the egg white mixture whip until cool.
Once the egg white mixture has reached room temperature, turn the mixer off and fold in the peanut butter and chopped peanuts. Use immediately or store in the refrigerator in an airtight container.