Trim the very bottom off the green garlic, and cut the stalk just below where the leaves start to protrude—in total the whole thing should measure about 8-10”, more or less. Peel apart all the leaves to expose the scape, and cut the bud from the stem. Peel off the first outer layer of the green garlic.
Take the leaves, peeled outer layer, scape bud, and any other garlic scraps into a saucepan with the asparagus ends, Parmesan rind, and water. Place over medium heat, and bring to a simmer. Season with ½ t-spoon kosher salt, and keep it at a simmer for 30 minutes on medium/medium-low. After 30 minutes, strain through a fine mesh sieve lined with cheesecloth—you should have 3 cups left. Pour this back into a pot and put over low heat, covered, to stay warm.
Separate the white bulbous bottom from the light green stalk of the green garlic; finely chop the bulb and thinly slice the green stalk. Use a vegetable peeler to peel thin strips of the scape before cutting them into slightly large bite-sized pieces.
In a heavy-bottom pan, such as a Dutch oven, heat 2 ½ tablespoons of butter, a few drops of oil, and finely chopped green garlic bulb over medium-low heat until fragrant—about 5-7 minutes.
Scatter the rice into the pan along with the sliced green garlic stalk—holding back a few paper-thin ones for serving—and peeled scape stem. Toss it in the butter until it’s slicked and glossy. Toss it around for another minute or two before pouring in the wine or vermouth. Stir it into the rice until it’s absorbed completely.
Now, ladle by ladle, add the broth you whipped up earlier, stirring constantly, and letting the rice absorb all the liquid before adding any more. I usually stir each ladle until it’s mostly absorbed, then leave the rice to full absorb what’s left before adding more. In all, it should take about 20 – 22 minutes.
Once the rice is tender and has absorbed the liquid, grate a few miniscule flicks of lemon zest into the rice, plop in the remaining ½ tablespoon of butter, and a bit of the Parmigiano-Reggiano, shut the heat off, and stir everything to combine.
Scatter with a little parsley and serve up into warmed bowls immediately, garnishing with a some of the reserve green garlic stalks you thinly sliced.
For the broth: the asparagus ends I have are fairly thick, and about 3" long. If yours are shorter, or thin, shorten the cooking time and reduce the amount of water by a few spoonfuls, more or less. The same goes for if you're using unfrozen ends, leftover from earlier in the week or something.
If you're not using asparagus scraps in the broth, or don't have any, don't worry; throw another Parmigiano rind in the broth, or maybe some parsley stems.