Scatter feta on a baking sheet. Char cheese with a blowtorch until browned, then refrigerate while you make the vinaigrette.
Puree strawberries in a blender until smooth, then pass through a mesh strainer. Return strained berries to blender and add oil, vinegar, mustard, honey, sugar, and salt. Blend until smooth. Fold in tarragon.
Dress arugula with prepared vinaigrette, sprinkle with pine nuts, and toss. Top salad with feta and serve immediately.