1. Hard-boil the eggs: Place eggs in a single layer in a saucepan, cover with cold water by 1 inch. Bring to a rolling boil over high heat. Remove from heat, cover, and let sit for 10-12 minutes.

2. Prepare an ice bath: While eggs rest, fill a large bowl with ice water.

3. Cool and peel eggs: Transfer cooked eggs to ice bath using a slotted spoon. Cool completely for at least 5 minutes. Gently tap and roll each egg to crack shell. Peel under cold running water.

4. Chop the eggs: Chop hard-boiled eggs into a medium dice. Place in a large mixing bowl.

5. Prepare vegetables: Halve cherry tomatoes. Finely dice red onion. Chop cilantro or parsley. Add to the bowl with eggs.

6. Cube avocados: Halve avocados, remove pits, scoop out flesh, and dice into bite-sized pieces. Add to bowl.

7. Make the dressing: In a small bowl, whisk together mayonnaise (or Greek yogurt), Dijon mustard, lime or lemon juice, salt, and pepper.

8. Combine and mix: Pour dressing over the egg mixture. Gently fold until well combined, being careful not to mash avocado too much.

9. Taste and adjust: Adjust seasonings as needed, adding more salt, pepper, or lime juice if desired.

10. Serve immediately: For best flavor and texture, serve immediately. Optionally, chill for 15-20 minutes to let flavors meld.