Grate the zucchini and transfer it to a colander. Sprinkle with sea salt and allow zucchini to sit at least 1 hour (up to 3) to allow it to drain. Squeeze any remaining water out of the zucchini.: Right away you will notice the fresh vegetal scent as the zucchini hits the grater, and dampness will bead on the strands. Letting it sit with a sprinkle of salt draws out water, concentrating flavor and preventing a watery frittata. After about an hour the zucchini will feel markedly less slimy and more like packed threads, and you should squeeze firmly to remove remaining moisture. One common mistake is skipping the draining, which leads to a soggy, under set middle; be patient and press firmly with a clean towel or your hands to avoid that issue.
Preheat the oven to 375 degrees F, and add the oil to a 10-inch cast iron skillet. Spread the oil around the full surface and sides of the skillet (I use a paper towel). Place skillet on the stove top over medium heat.: As the oven warms, the cast iron will become evenly hot, which is important for even cooking and a crisp edge. Coat the skillet surface and sides with olive oil using a paper towel, spreading until it glistens but not pools. When the pan is hot on the stove at medium heat you may hear a faint sizzle if you touch a tiny drop of water to it; that sound means the skillet will promote a nice crust. A common error is using too much oil which causes the frittata to fry rather than bake, so a thin, even layer is best.
Place the arugula in the heated skillet and cover. Cook, stirring occasionally just until wilted, about 1 to 2 minutes. Remove from heat and allow arugula to cool.: The moment the arugula hits the warm oil it will begin to wilt and release a peppery aroma that fills the kitchen. Covering traps steam and shortens the wilting time to just one to two minutes, which keeps some of the bright flavor intact. Stir occasionally so the leaves wilt evenly and dark green patches form without becoming slimy. Avoid overcooking, as overly soft arugula loses its texture and turns pasty; remove the pan from heat promptly when it is just wilted.
Whisk the eggs, feta, and sea salt together in a mixing bowl. Add the grated zucchini, arugula, and chopped fresh herbs. Stir together until everything is well combined. Pour the egg and veggie mixture into the cast iron skillet and place on the center rack of the preheated oven. Bake 25 to 30 minutes, or until the center has set up and the top is beginning to turn golden-brown. Remove from the oven and allow frittata to rest 10 minutes before cutting and serving.: The bowl will take on a pale, frothy sheen as you whisk, and the aroma of salty feta cheese will mingle with the eggs. Whisk until the mixture is homogenous and slightly airy, which helps the frittata have a tender lift. Fold in the grated and squeezed zucchini , wilted arugula , and chopped herbs so they are evenly distributed. A frequent slip up is under seasoning; taste a tiny bit of the mixture or trust the salt, but remember that the feta cheese already contributes salinity, so balance is key.
Pour the egg and veggie mixture into the cast iron skillet and place on the center rack of the preheated oven: When the skillet goes into the oven you will see the mixture level out and small bubbles begin to form around the edges. Baking at 375 degrees F encourages even rise and a golden top without drying the interior. The visual cue you want is the center transitioning from glossy to matte and the edges pulling slightly away from the pan after about twenty five minutes. Avoid opening the oven too often, which causes temperature fluctuation and can yield uneven setting; trust the process and check near the end of the suggested bake time.
Bake 25 to 30 minutes, or until the center has set up and the top is beginning to turn golden brown: As the frittata bakes you will smell the melding of herbs and the tang of the feta cheese . The surface will go from wet to firm, with a few browned peaks showing through; that golden color signals Maillard reactions that add depth of flavor. The center should feel springy when gently nudged, not liquid; if it still jiggles, continue baking a little longer. A typical mistake is removing it too soon which leaves a runny middle, so allow it the full time if needed for a confident set.
Remove from the oven and allow frittata to rest 10 minutes before cutting and serving: Resting is a quiet step where the residual heat finishes the cooking gently, yielding a creamier texture and easier slicing. In those ten minutes the steam redistributes and the flavors settle, so when you cut wedges they hold together without crumbling. If you slice immediately, the interior can be loose and messy, so patience here improves presentation and mouthfeel.