Put the balsamic vinegar in a small saucepan and bring to a simmer over medium-high heat. Cook until the vinegar is reduced to about 1/3 cup and syrupy, about 15 minutes; cool to room temperature.
Remove the feathery fronds from the fennel bulb and chop. Remove the core from the fennel and, using a mandoline slicer or a knife, shave the fennel into very thin slices. Add to a salad bowl along with the arugula and almonds. Drizzle the reduced vinegar over the greens, season with salt and pepper, to taste, and toss until coated. Sprinkle the strawberries and chopped reserved fennel fronds over the top and serve immediately.