The pasta dough is easily made in a food processor with a metal blade and then rolled out with a metal pasta maker. Put the flour in the food processor followed by the eggs, 3 tablespoons olive oil, and the water. Process until a rough ball of dough forms. Transfer to a floured work surface and knead until elastic, 6 or 7 minutes. Wrap loosely in plastic wrap or aluminum foil and let stand at room tempature for 30 minutes.

Divide the dough into balls each about the size of a walnut. Keep them loosely covered with a damp cloth. Set the pasta machine rollers at the widest setting, dust the roller with flour and run a ball of dough through them. Reset the rollers to a medium setting and run the sheet through again. Lay the pasta sheet on a piece of floured waxed paper and arrange some of the whole basil leaves and about 2 tablespoons of the blossoms on it. Roll out a second pasta sheet in the same way. Lay the second sheet over the first sheet and gently press together to hold the leaves and blossoms in place. Run this doubled sheet through the rollers, first on a medium setting, then on the next to the narrowest. Lay the sandwiched sheets on a floured surface and cover lightly with a damp kitchen towel. Repeat until all the dough has been used. Using a sharp knife, cut the sheets into long 1/2-inch-wide strips.

Bring a large saucepan three-fourths full of water to a boil. Add the salt and the pasta, stir well, and cook until al dente, 2 to 3 minutes.

Drain the pasta and place in a warmed bowl or on a serving platter. Add the extra-virgin olive oil, butter, salt, pepper, and the chopped basil, and turn gently. Garnish with the 1 tablespoon blossoms and serve immediately.