Wash kale leaves and spin-dry in a salad spinner. Remove the stems and tear the leaves into bite-sized pieces. Place them in a large mixing bowl.
2 large bunches kale
Cut cherry tomatoes in half and place them in the bowl with the kale.
2 pints cherry tomatoes
Heat a grill to medium high heat. Salt and pepper the chicken breast and grill each side for 6 minutes or until cooked. Shred the chicken.
4 Chicken breasts, Salt, Freshly ground black pepper
For the dressing, place the egg yolks, mustard, garlic, anchovies, lemon juice, salt, and pepper into the bowl of a food processor fitted with a steel blade. Process until smooth. With the food processor running, slowly pour the olive oil through the feed tube (as though you were making mayonnaise), until thick. Add the grated Parmesan cheese and pulse 3 times.
1 extra-large egg yolk at room temperature, 2 teaspoons Dijon mustard, 2 large cloves garlic, 8 to 10 anchovy fillets, 1/2 cup freshly squeezed lemon juice, 2 teaspoons kosher salt, 1/2 teaspoon freshly ground black pepper, 1 1/2 cups good mild olive oil
Toss the kale with enough dressing to moisten well. Add 1 cup grated Parmesan and toss. Divide the kale among 6 or 8 plates and sprinkle with the grilled chicken and cherry tomatoes. Serve at room temperature.
1/2 cup freshly grated Parmesan cheese
All these ingredients can be made in advance. Be sure they're room temperature when you assemble the salad.
If you're nervous about raw egg yolks, substitute 2 tablespoons of real mayonnaise.