Combine 4 cups of water and 4 cups of ice in a large mixing bowl.
In a Dutch oven, boil 3 quarts of water. Pour out 1 cup of boiling water and put this in a small bowl to soak the figs. Cover and let it sit for 5 minutes and drain afterwards.
Add broccoli stalks to the boiling water and cook no longer than 1 minute. Add in the florets and cook until slightly tender for about 1 minute.
Drain the broccoli and place in ice water to cool.
Once cool, drain again and transfer to salad spinner and spin dry.
Whisk the yogurt, vinegar, salt and pepper in a large bowl. Add broccoli, drained figs, walnuts and shallots to the bowl with dressing and toss to combine.
Season with salt and pepper to taste.