Begin by trimming the tops and bottoms of the oranges to create a stable base. Use a sharp knife to carefully peel away the outer skin, ensuring no pith remains. Once peeled, gently cut along the membranes to release the citrus segments. Set the supremes aside.

Open the can of hearts of palm and drain the liquid. Pat the palm hearts dry with a clean kitchen towel. Slice them into ½-inch rounds.

Thinly slice the English cucumber and radishes. Cut the radishes into matchsticks. Finely chop the shallots.

In a large mixing bowl, combine the arugula, sliced hearts of palm, cucumber, matchstick radishes, shallots, and the freshly prepared orange supremes. Gently toss the ingredients together.

Drizzle the lemon vinaigrette over the salad mixture, ensuring an even coating. Gently toss the salad with your hands or tongs for about 30 seconds.

Divide the mixture onto individual plates or a large serving platter. Top each serving with slices of avocado, sprinkling grated Parmesan cheese over the top. Drizzle with additional vinaigrette if desired.