Mix the flour and eggs together in a bowl, then knead until the dough is smooth and elastic, about 8 minutes. Wrap in plastic and let rest for 30 minutes to relax the gluten.
While the dough rests, finely chop the cooked lobster meat. In a skillet, melt the butter over medium heat, add minced garlic, and cook until fragrant, about 1 minute. Remove from heat, then stir in the lobster, lemon zest, chopped herbs, and a squeeze of lemon juice. Season with salt and pepper to taste. Chill the filling for 15 minutes.
Divide the rested dough into four portions. Using a pasta roller or rolling pin, roll each piece out to about 1 mm thick, dusting with flour to prevent sticking. Keep the sheets covered as you work to prevent drying out.
Place teaspoon-sized dollops of the lobster filling evenly spaced on one sheet of pasta. Brush the edges with a little water, then carefully cover with another pasta sheet. Press gently around each mound to seal, removing excess air. Cut into individual ravioli using a cookie cutter or ravioli stamp.
Bring a large pot of salted water to a boil. Carefully drop the ravioli in and cook for 3–4 minutes, or until they float to the surface and are tender. Use a slotted spoon to remove them gently.
In a frying pan over medium heat, melt the butter until it turns golden brown and emits a nutty aroma, about 2–3 minutes. Add a squeeze of lemon juice and stir to combine. This will create a fragrant browned butter sauce.
Place the cooked ravioli on serving plates. Drizzle generously with the browned butter sauce, then garnish with additional herbs or lemon zest if desired. Serve immediately to enjoy the tender pasta and luscious filling.
