Preheat and prep: Preheat the oven broiler (or prepare a lid for the skillet). Crack 4 large eggs into a medium bowl and whisk gently until homogeneous—you want the whites and yolks fully combined for an even texture. Season with a light pinch of kosher salt and several grinds of black pepper. Whisking introduces air that will make the frittata tender and uniform.

Prep the vegetables: Finely chop 60 g lacinato kale (remove the tough center ribs), thinly shave 50 g fennel, and thinly slice two small shallots. If using the optional garlic, mince 1 small clove. Dry vegetables sear better than wet ones—pat them with a towel if washed. Chopping uniformly ensures even cooking and a pleasing texture in every bite.

Cook the aromatics: Heat a 9–10 inch (23–25 cm) ovenproof nonstick or well-seasoned cast-iron skillet over medium heat. Add 2 tsp extra-virgin olive oil and once warm (shimmering, not smoking), add the shallots and optional garlic. Sauté 2–3 minutes until translucent and fragrant. This step softens the shallot and draws out sweet aromatics that form the flavor base.

Sweat the fennel and kale: Add the shaved fennel and chopped kale to the skillet and season with a small pinch of salt. Cook, stirring, 3–4 minutes until the fennel softens and the kale wilts. You want just enough cooking so the vegetables are tender but still bright—overcooking will make them limp and reduce contrast with the eggs.

Cool slightly, then combine: Remove the skillet from heat to cool 30–60 seconds (this prevents the eggs from immediately scrambling on contact). Stir the cooked vegetables into the whisked eggs along with 2 tbsp grated Parmigiano-Reggiano and 2 tsp chopped fresh thyme. The cheese adds savory umami and helps the eggs set with creaminess; thyme gives a warm, herbaceous lift.

Brown the base: Wipe the skillet clean and return to medium-low heat; add 2 tsp (≈9 g) butter and let it melt and foam—this nutty butter flavor will accent the frittata. Pour the egg-vegetable mixture into the skillet and gently spread so it's even. Cook undisturbed 2–3 minutes until the edges begin to set and pull away slightly from the pan. Cooking on medium-low ensures a gentle set without overbrowning; a higher heat will give a rubbery texture.

Finish on the top: When edges are set but center still jiggly, transfer the skillet to the oven under the broiler for 1–3 minutes, watching closely, until the top is puffed, lightly golden, and cooked through. If you don't have a broiler-safe skillet, cover with a lid and finish on the stovetop over very low heat for 4–6 minutes. The brief broil adds a golden surface color and quick finish without drying the interior.

Rest and slice: Remove the skillet and let the frittata rest 2 minutes—this helps the eggs finish cooking and results in cleaner slices. Run a spatula around the edges and slide onto a cutting board or serve straight from the skillet for a rustic presentation. A short rest also lets flavors meld.

Grill the sourdough: While the frittata finishes, heat a separate skillet or griddle over medium-high. Brush both sides of each sourdough slice with the remaining 1 tsp extra-virgin olive oil (split) or a little butter if you prefer, and grill 1–2 minutes per side until deep golden and crisp. The grilled bread gives a toasty crunch and a vehicle for the silky frittata.

Finish and serve: Cut the frittata into two wedges. Plate each wedge with a grilled sourdough slice, a lemon wedge on the side, and a light sprinkling of extra Parmigiano and a few turns of black pepper. A squeeze of lemon just before eating brightens the dish and balances the richness.