After about 2 minutes…
5. USE a slotted spoon to remove the egg and set aside in a warm bowl of water. Cook the eggs just under of how you’d normally like your eggs. Repeat with the remaining eggs. Once done, cover the pot and turn the heat down to low to keep the water hot.
When the lentils are tender…
6. REMOVE the thyme sprigs and bay leaf. Drain any excess stock that may remain. Season with kosher salt and black pepper as needed. Toss the lentils with the arugula leaves and use a slotted spoon to plate into 4 dishes. Using the slotted spoon…
7. DIP each poached egg into the pot of hot water to rewarm it. Gently blot them dry with a paper towel and place on top of each lentil mound. Place Parmesan cheese shards over plate and drizzle the tops with a bit of the olive oil. Garnish with additional thyme sprigs and serve immediately.
FOOD TRIVIA: THE DIFFERENCE BETWEEN PARMESAN AND PARMIGIANO REGGIANO
In the European Union, Parmigiano-Reggiano is a D.O.P.-protected term that can only be used by members of the Consorzio del Formaggio Parmigiano-Reggiano, which approves each and every wheel of cheese as meeting the highest Consorzio standards (substandard cheeses are removed from the process before aging concludes).
However, in 2008 the E.U. also defined the term “Parmesan” to refer to the genuine Consorzio cheeses. Prior to then, Parmesan referred to Parmigiano-Reggiano-style cheeses made outside the D.O.P.-designated regions of Emilia-Romagna and Lombardy. Thus, within the E.U., Parmesan and Parmigiano-Reggiano are the same cheese. (Why ask why?)
In the U.S. and other parts of the world, the word “Parmesan” is not regulated. A cheese labeled as Parmesan in the U.S. is a domestic cheese approximating Parmigiano-Reggiano.
Why is the word capitalized? It’s an editorial choice. Both Parmesan and Parmigiano are adjectival forms of Parma, the city in the Italian region of Emilia-Romagna where the cheese originated. We would apply the same style, for example, to an Iowan cheese or a Chicagoan cheese (as opposed to an iowan cheese or chicagoan cheese).
Here’s more about Parmigiano-Reggiano cheese.