Begin by blanching the parsley. This is so that it will stay green and vibrant even while it dresses hot cabbage in a hot broth.
To do this, bring a large pot of water to a boil. Prepare an ice bath to the side. Season the boiling water with a large pinch of kosher salt. Submerge the parsley (stems and all) in the boiling water for 30 seconds, then use tongs to transfer it to the ice bath.
Squeeze out any excess water from the parsley and finely chop it. Transfer it to a bowl.
Grate 1/2 teaspoon of lemon zest into the parsley (about 1/4 of a lemon). Cut the top and bottom of the lemon off, making both slices big enough to still hold a little juice. Set all the pieces to the side.
Halve the garlic crosswise. Set aside the bottom of the garlic, and pop out the cloves from the top to grate into the parsley mixture. Set the parsley mixture in the fridge.
Remove the top and bottom of the shallots and halve them lengthwise. Remove the green parts from the leek and halve the white part lengthwise.
Drain the pot you boiled the parsley in. Set it back over medium heat and coat the bottom with 1/4 cup of olive oil. Let this heat up for a few minutes.
Place the center of the lemon, the bottom of the garlic, the shallots and the leek into the hot oil, searing them all cut-side-down for 3-4 minutes or until they are deeply golden brown. Flip and sear the other sides, making sure the lemon is caramelized on both sides.
Add the oregano, thyme, bay leaves, red pepper flakes and parmesan rinds to the pot. Cover with 8 cups of water. Bring this to a simmer and season with 2 teaspoons of kosher salt.
Let this simmer for 60-90 minutes to make the parmesan broth. The longer it goes, the more flavor it will build.
When the broth has 45 minutes left, preheat the oven to 425°F.
Thinly slice the cabbage and add it to an unlined baking sheet. It's ok if it's a little crowded. Drizzle with olive oil, season with salt and mix to coat.
Roast the cabbage for 20-30 minutes or until golden and crispy on the edges and softened in the center.
While the cabbage is roasting, remove the parsley mixture from the fridge. Finely chop the capers and add them in, along with the juice from the two lemon wedges, the white wine vinegar, a large pinch of salt and a few cracks of black pepper. Drizzle in three tablespoons of olive oil. Taste and season with more salt, pepper and vinegar as preferred.
When the cabbage is out of the oven, pour the parsley dressing all over it. Mix to coat.
At this time the parmesan broth should be done. Use a slotted spoon to skim all the ingredients out of the pot, leaving behind just the rich umami broth. Taste and season with salt as needed.
To serve, pile the herby cabbage in a bowl. Pour the parmesan broth right over it and grate on some more fresh parmesan. Serve warm.