Combine lemon juice, Dijon mustard, shallot, garlic, ½ tsp. 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 ½ cup oil into a cup. Spoon 1 Tbsp. 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.
Add dressing and cheese to kale mixture; toss to coat. Season lightly with salt and pepper. Garnish with almonds.
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.
