1/4 cup fresh lemon juice
2 tablespoons Dijon mustard
1 tablespoon minced shallot
1 small garlic clove, finely grated
1/4 teaspoon kosher salt plus more for seasoning
Freshly ground black pepper
2 large bunches of Tuscan kale (about 1 1/2 pounds total), center stem discarded, leaves thinly sliced
12 ounces brussels sprouts, trimmed, finely grated or shredded with a knife
1/2 cup extra-virgin olive oil, divided
1/3 cup almonds with skins, coarsely chopped
1 cup finely grated Pecorino or Parmesan
Combine lemon juice, Dijon mustard, shallot, garlic, 1/4 teaspoon salt, and a pinch of pepper in a small bowl. Stir to blend; set aside to let flavors meld. Mix thinly sliced kale and shredded brussels sprouts in a large bowl.
Measure 1/2 cup oil into a cup. Spoon 1 tablespoon oil from cup into a small skillet; heat oil over medium-high heat. Add almonds to skillet and stir frequently until golden brown in spots, about 2 minutes. Transfer nuts to a paper towel-lined plate. Sprinkle almonds lightly with salt.
Slowly whisk remaining olive oil in cup into lemon-juice mixture. Season dressing to taste with salt and pepper. DO AHEAD: Dressing, kale mixture, and toasted almonds can be prepared 8 hours ahead. Cover dressing and kale mixture separately and chill. Cover almonds and let stand at room temperature.
Add dressing and cheese to kale mixture; toss to coat. Season lightly with salt and pepper. Garnish with almonds.