1. Boil a large pot of salted water; add homemade cavatelli carefully, and cook, uncovered, 5 minutes or until pasta is almost tender, stirring gently. Stir in asparagus, and cook 2 minutes or until crisp-tender. Set a large, shallow pasta bowl in the sink; place colander in the bowl. Pour pasta and asparagus into the colander to drain, reserving 1/4 to 1/2 cup cooking water. (This also warms the serving bowl.)
2. Heat oil and garlic in a large, deep skillet over medium-low heat 1 minute. Reduce heat to low, and cook 5 minutes, being careful not to brown garlic. Turn off heat. Stir in tomato and basil; discard garlic. Spoon pasta and asparagus into skillet; stir gently over medium heat 2 minutes or until combined. Add reserved pasta liquid, a little at a time, as needed to moisten pasta.
3. Pour water out of serving bowl; wipe dry, and fill with pasta. Add cheese and arugula; toss to combine. Add salt and pepper, and serve immediately.
*For testing purposes, we used Precious Brand whole milk ricotta. If ricotta isn't available, substitute with a mild feta or Pecorino Romano.