In a small bowl, combine flour, egg yolks, 2 tablespoons olive oil and milk. Hand mix until well combined and slightly elastic; add more cold milk if too dry or add more flour if too wet. Roll into a tight ball, wrap with plastic wrap and refrigerate for 5 hours.
When ready to make the fettuccine, roll dough out on lightly floured board and use a pasta machine to cut the fettuccini into ¼-inch strips. Bring large pot of water to boil; drop pasta to cook for 2–3 minutes before serving.
Remove lobster meat from claws and tail and cut into medallions; reserve bodies to flavor the sauce. Heat large pot over medium heat, add 4 tablespoons olive oil and onions and cook until onions are translucent. Increase heat to high, add lobster bodies and sauté for 15 minutes. Add Cognac to deglaze pot. Add garlic, parsley, chili flakes and cherry tomatoes, and cook for 10 minutes. Add tomato paste and white wine and cook for 5 minutes. Add fish stock and cook on high heat for 10 minutes. Remove and discard lobster shells. Add salt and pepper to taste. Add lobster meat medallions and simmer for 2–3 minutes. Add chopped basil and remove from heat.
Divide fettuccini into four large shallow bowls and top with lobster medallions and sauce. Garnish with whole basil leaves. Serves 4.
Saints Hills 2019 Posh St. Ante Vineyard Posip (Croatia); $29, 90 points. This Croatian white is made from the indigenous Posip grape. It is pale straw in color with aromas of lemon zest, river rock, mandarin orange and lemon grass with just a whiff of dried Mediterranean herbs. It is soft on entry but very full-bodied in the mouth with flavors of vanilla, lemon curd and grapefruit. It is well balanced with nice minerality and a touch of salinity on the finish.