Trim the cauliflower, reserving the stem to make your purée. Cut the head of cauliflower into 1-inch-thick “steaks.”

Make your purée: Place the reserved cauliflower stem in a large pot, then cover it with water and season with salt. Bring the water to a boil over high heat, then cook until the stem is soft and tender, about 20 minutes. Reserve ½ cup of the cooking liquid, then strain the stem.

Transfer the cauliflower stem to a blender and add 1 tablespoon of the butter. Blend on high until smooth, then season with salt to taste. If the purée is too thick, blend in 2 tablespoons of the cooking liquid until the mixture reaches your desired consistency.

Prepare your chicken: Debone the chicken thighs, if needed. Place the chicken between 2 large pieces of plastic wrap. Using a meat mallet or heavy pan, pound the chicken to about ½-inch thickness. Season the chicken with the cardamom and more salt.

Prepare the breading: To a shallow bowl, add the flour. Crack the eggs into a second shallow bowl and whisk them to combine. In a third shallow bowl, mix together the breadcrumbs and oregano.

Working 1 piece at a time, dip the chicken into the flour, then the eggs, then the breadcrumbs.

Heat 1 cup of vegetable oil in a large skillet over medium heat until the temperature reaches 350ºF. Gently add the chicken to the hot oil and fry until golden and cooked through, 4 minutes per side. Transfer the cooked chicken to a paper towel–lined plate to drain.

Peel the butternut squash. Using a mandolin, slice the squash into thin shavings. If you prefer, you can cut the peeled squash into a small dice, then blanch for 5 minutes and shock it in an ice bath.

In a large bowl, combine the arugula and the squash. Drizzle with the lemon juice and as much olive oil as you like, then season with salt to taste. Toss to combine.

Cook the cauliflower “steaks”: Preheat a separate large pan over medium-high heat. Drizzle the pan with enough vegetable oil to coat the bottom, then reduce the heat to medium. Add the cauliflower “steaks” and sear until browned, 3 minutes per side. Add the fresh thyme sprigs and 1 tablespoon of butter to the pan and cook, basting the cauliflower with the melted butter, for a few minutes more. Remove and discard the thyme sprigs from the pan.

Make the sauce: In a small pan, heat the broth over medium-high heat. Cook until reduced by half, then add 1 tablespoon of butter and the Dijon mustard. Whisk until fully incorporated.

Serve the crispy chicken thighs with the cauliflower “steaks,” purée, sauce, and shaved butternut squash salad.