Step 1

Melt lard in 8-inch skillet over medium-low heat. Add garlic and cook, swirling skillet and flipping garlic occasionally, until garlic is pale golden brown, 7 to 10 minutes. (Tiny bubbles will surround garlic, but garlic should not actively fry. Reduce heat if necessary.) Turn off heat, but leave skillet on burner. Discard garlic.

Step 2

While garlic cooks, bring 2 quarts water to boil in large saucepan. Beat eggs in medium bowl until very few streaks of white remain. Stir in Parmesan, Pecorino, parsley, salt, and pepper and set aside.

Step 3

Stir pasta and 1½ teaspoons salt into boiling water and cook, stirring often, until pasta is tender (slightly past al dente). Reserve ¼ cup cooking water, then drain pasta and return it to saucepan. Immediately add lard, egg mixture, and 1 tablespoon reserved cooking water to pasta and stir until cheese is fully melted. Adjust consistency with remaining reserved cooking water, 1 tablespoon at a time, as needed. Serve immediately.