To boil eggs in an electric slow cooker, follow these steps:

1. Begin by filling the slow cooker with water, ensuring that the eggs are fully submerged. The water level should be about 1 to 2 inches above the eggs.

2. Set the slow cooker to the "High" setting and let it come to a boil. This process typically takes about 2 to 3 hours.

3. Once the water is boiling, reduce the temperature to the "Low" setting and continue cooking for another 2 to 3 hours. This allows the eggs to cook through evenly.

4. After the cooking time has elapsed, carefully remove the eggs from the slow cooker using tongs or a slotted spoon. Place them in a bowl of ice water to stop the cooking process and prevent overcooking.

5. Let the eggs sit in the ice water for about 5 minutes, then peel and serve.

Boiling eggs in an electric slow cooker is a convenient and hands-off method that ensures even cooking. The slow and steady heat of the slow cooker prevents the eggs from cracking and ensures that they are fully cooked without the risk of burning. According to the USDA, eggs should be cooked to an internal temperature of 160°F (71°C) to ensure safety. The slow cooker's ability to maintain a consistent temperature over a long period of time makes it an ideal appliance for this task. Additionally, the use of ice water after cooking helps to stop the cooking process quickly, which is crucial for maintaining the texture and flavor of the eggs.