Add the potatoes, carrots, and the raw eggs to a large stockpot. Fill the pot with cold water, making sure the water fully covers the potatoes and eggs. Bring the water to a gentle boil over medium-high heat. After the water in the pot comes to a boil, reduce the temperature to medium-low. Simmer the potatoes and eggs for 12-15 minutes, or until the potatoes are fork-tender and fuly cooked

Drain the potatoes, carrots and eggs in a colander set inside a sink. Place the eggs in a bowl with cold water. Once they're cool to the touch, peel the eggs and set aside.

Allow the potatoes and carrots to drain and cool in the colander at room temperature.

In a bowl, toss the diced apple pieces with the vinegar and let them sit for 5 minutes. This step will prevent the apples from turning brown.

Add the red onion, bell pepper, mayo, salt and pepper into the bowl with the apples, and stir with a spatula until smooth.

Peel, then chop the hard-boiled eggs after they've cooled slightly.

Add the eggs, potatoes and carrots to the bowl with the dressing. It's okay if the potatoes are still warm, this will help them absorb the dressing better.

Fold the potatoes and eggs into the dressing mixture until they're evenly coated. Add more mayonnaise if you like. Cover the potato salad with plastic wrap or foil and transfer it to the fridge. Chill the potato salad for 8 hours (overnight is best).

When you're ready to serve it, stir the potato salad to make sure it's not too dry. If you find your potatoes have soaked up too much of the mayo, add more mayo on top and stir it in. Taste for salt, and adjust as needed. Garnish with green onions and roasted red pepper slices, if desired.