Mound flour on work surface or in large bowl and make well in center. Add eggs to well and blend with fork. Gradually draw flour from inner edge of well into center until all flour is incorporated. Gather dough into ball. Cut dough into 3 pieces. Flatten 1 piece (keep remainder covered), then fold into thirds. Turn pasta machine to widest setting and run dough through 10 times until smooth and velvety, folding before each run and dusting with flour if sticky. Adjust machine to narrower setting. Run dough through machine without folding. Repeat narrowing rollers after each run until pasta is 1/16 inch thick, dusting with flour as necessary. Hang dough on drying rack or place on towels. Repeat with remaining dough. Dry sheets until leathery and edges begin to curl. Pasta must be cut at this point or it will be too brittle. Run sheets through thinnest blades of pasta machine to cut. Arrange strands on towel, overlapping as little as possible. Boil cream with cheese until reduced to 1-1/2 cups. Set aside. Season scallops with salt and pepper. Melt butter in large skillet over high heat. Saute scallops on both sides until firm, about 1 minute. Cook pasta in large amount of rapidly boiling salted water until just tender but firm to bite. Drain well. Reheat cream mixture. Set aside 8 scallops, 20 asparagus and 2 tablespoons basil. Stir remaining scallops, asparagus and basil into sauce. Add to pasta and toss well. Season generously with salt and pepper. Mound pasta on plates. Decorate with reserved scallops, asparagus and basil. Sprinkle with fresh chives. Makes 8 servings.