Preheat oven to 425°F with racks in the upper and lower thirds.
Slice golden beets into 1/4-inch rounds and red beets into 1/2-inch wedges.
On separate baking sheets, toss each type of beet with 1/2 Tbsp olive oil and 1/8 tsp salt. Arrange in single layers and roast for 22–24 minutes, rotating halfway. Red beets may need 2 extra minutes.
In a small bowl, mix sliced shallot, lemon zest, lemon juice, and a pinch of salt. Let sit while beets roast. Stir in honey and remaining 1 Tbsp olive oil.
In a large bowl, toss baby arugula with dressing. Gently fold in roasted beets and orange slices.
Top with chopped pistachios, flaky salt, and shaved ricotta salata before serving.