Toast walnuts in small skillet over medium heat, mixing occasionally. Cool. Chop coarsely.
Whisk lemon juice, mustard, shallot, garlic, 1 tsp. salt, and 1/2 tsp. pepper in a medium bowl, then whisk in oil in a slow, steady stream. Adjust salt and pepper to taste. Set aside.
Mix together kale and Brussels sprouts in a large mixing bowl. Add about 3/4 of the dressing, and use your hands to massage dressing into greens. Taste and add more dressing as needed Reserve any leftover dressing for another use.
Add apple and half of walnuts; toss together to combine. Transfer to a serving bowl, and top with nuts and remaining radishes.
Do ahead
Dressing can be prepared 3 days ahead; cover and chill. Nuts can be toasted and chopped 1 day ahead; cover and keep at room temperature. Kale and Brussels sprouts can be sliced 1 day ahead; place in an airtight container and chill. Salad can be tossed together 30 minutes ahead; keep at room temperature.