Step 1

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.

Step 2

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.

Step 3

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.

Step 4

Add dressing and cheese to kale mixture; toss to coat. Season lightly with salt and pepper. Garnish with almonds.