Over medium high heat, bring salted water to a boil in a large pot.
While waiting for the water to boil, cut the top and bottom off of the zucchini and discard. Cut the zucchini in half crosswise. Then, place the zucchini on a flat side so it's standing up straight. Slice lengthwise straight down, creating long zucchini strips that are about 1/2 inch think. Slice all of the zucchini and place into a mixing bowl.
Pour about 1 tbsp of olive oil onto the zucchini and add some salt and pepper to taste. Toss the zucchini slices in the olive oil, salt and pepper, until fully coated.
Heat a grill pan over high heat. (If you have a regular grill, good for you!!! Use that instead :D) Once the pan is piping hot, place the zucchini strips onto the pan, in the opposite direction of the grooves. Let the zucchini sit until char marks distinctly form on the down-facing side. Flip after about 5 minutes, or until charred to your liking. Repeat on the other side.
Once the water is boiling, add the eggs and let them boil for 7 minutes. Remove and place in a bowl of cold water (you can also do the traditional ice bath technique, but I find it to be a lot of work that isn't necessary.) You also can just run the eggs under cold water until they aren't piping hot to touch.
Remove the zucchini from the pan and plate however you see fit.
Crack the eggs by rolling them onto the countertop lightly. Peel the eggs by starting from the wider side of the egg, as it helps the eggs peel more easily.
Slice the eggs horizontally, and plate on top of the zucchini with salt and pepper. Drizzle avocado chimichurri on top and plate with fresh herbs.