Cook bacon in 10-inch skillet over medium heat until crisp, 6 to 8 minutes. Drain on paper towel–lined plate.
Bring 3 quarts water to boil in Dutch oven. Remove 1 cup boiling water and combine with figs in small bowl; cover, let sit for 5 minutes, and drain.
Combine 4 cups water and 4 cups ice in large bowl.
Add broccoli stalks to boiling water and cook for 1 minute. Add florets and cook until slightly tender, about 1 minute. Drain broccoli and place in ice water to cool. Drain again, transfer to salad spinner, and spin dry, or lay out on a clean kitchen towel to dry.
Whisk mayonnaise, vinegar, ½ teaspoon salt, and ¼ teaspoon pepper together in large bowl.
Add broccoli, drained figs, walnuts, and shallot to bowl with dressing and toss to combine.
Season with salt and pepper to taste. Sprinkle with bacon and serve.
Salad may be made up to 6 hours in advance.