Prepare the Vinaigrette: In a small bowl or a glass jar with a lid, combine all vinaigrette ingredients: extra virgin olive oil, fresh orange and lemon juices, orange zest, grated garlic, and black pepper. Whisk vigorously or shake the sealed jar until the mixture is well-combined and lightly emulsified. Set aside to allow the flavors to meld.
Segment the Oranges: Using a sharp paring knife, slice off the top and bottom of the oranges. Stand an orange on one flat end and carefully slice downwards, following the curve of the fruit, to remove all the peel and white pith. Over a bowl to catch any juices, hold the peeled orange and carefully cut between the membranes to release the individual segments. Place the segments in a large mixing bowl.
Prepare the Fennel: Trim the fronds and the tough base from the fennel bulbs. Halve the bulbs lengthwise and remove the core. Using a mandoline on a very thin setting (or a sharp knife), shave the fennel into paper-thin slices. Add the shaved fennel to the bowl with the orange segments.
Combine the Core Ingredients: Add the rinsed and drained chickpeas and the rinsed Kalamata olives to the bowl containing the orange segments and fennel.
Dress the Salad: Pour about two-thirds of the prepared vinaigrette over the ingredients in the mixing bowl. Using your hands or silicone spatulas, gently toss everything together until just coated. Be careful not to break the delicate orange segments.
Assemble and Serve: Arrange the arugula on a large serving platter to create an even bed of greens. Artfully spoon the dressed fennel, orange, and chickpea mixture over the top. Drizzle the remaining vinaigrette evenly over the entire salad. Garnish generously with fresh mint leaves and serve immediately.