Preheat a grill or a grill pan over medium-high, and lightly coat with vegetable oil. In a large bowl, toss the kale with 2 Tbsp. olive oil, and season with salt and pepper.
Place the lemons on the heated grill, cut sides down, and grill until charred, about 5 min. Transfer to a plate. Meanwhile, add the kale to the grill, working in batches if necessary, and cook until tender and golden in places, flipping halfway through, about 1 min. per side. Transfer kale to a large serving platter.
In a medium bowl, squeeze 2 Tbsp. juice from the grilled lemons; save remaining lemons for serving. Whisk the remaining 4 Tbsp. olive oil and the garlic into the lemon juice. Stir in the asparagus, pomegranate seeds, mint, and pistachios; season with salt and pepper.
Dollop asparagus relish over grilled kale, and serve with extra grilled lemons on the side.
Recipe by Laura Rege.