To achieve a boiled egg with a fully cooked egg white and a partially cooked, runny egg yolk (often referred to as a "soft-boiled egg"), you can follow these steps:

1. **Prepare the Eggs:** Start by selecting fresh eggs at room temperature. If the eggs are cold from the refrigerator, allow them to sit at room temperature for about 10-15 minutes before cooking.

2. **Boil Water:** Fill a saucepan with enough water to cover the eggs completely. Bring the water to a rolling boil over medium-high heat.

3. **Add the Eggs:** Gently lower the eggs into the boiling water using a spoon or egg holder to prevent them from cracking. Be careful not to overcrowd the saucepan, as the eggs need space to cook evenly.

4. **Boil Eggs:** Once the eggs are in the boiling water, reduce the heat to medium to maintain a gentle boil. Set a timer for 6-7 minutes for a soft-boiled egg with a partially cooked yolk. Adjust the timing slightly based on your preference for the consistency of the yolk.

5. **Prepare an Ice Bath:** While the eggs are boiling, prepare a bowl of ice water large enough to submerge the eggs completely. This ice bath will stop the cooking process and help prevent overcooking.

6. **Transfer Eggs to Ice Bath:** When the timer goes off, immediately remove the eggs from the boiling water using a slotted spoon and transfer them to the ice water bath. Allow the eggs to cool in the ice water for about 1-2 minutes to halt the cooking process.

7. **Peel and Serve:** After cooling, gently tap each egg on a hard surface to crack the shell, then peel the shell under running water or in the ice water bath. Carefully remove the shell to reveal the soft-boiled egg with a partially cooked, runny yolk.

8. **Season and Enjoy:** Season the soft-boiled eggs with a pinch of salt and pepper, if desired, and serve immediately. Soft-boiled eggs are delicious on their own or served with toast, salads, or as part of a breakfast or brunch spread.

By following these steps, you can achieve a soft-boiled egg with a fully cooked egg white and a partially cooked, runny egg yolk, perfect for dipping toast or enjoying as a nutritious snack. Adjust the cooking time slightly to achieve your desired level of yolk doneness.