Thoroughly wash the oranges, then use a mandoline or sharp knife to slice to 4-5mm thickness. If you feel like your oranges are too soft to cut evenly, place them in the freezer for about 30 minutes to help them firm up before slicing.
Bring a medium pot or sautée pan with 6 cups of water to a boil. Boil the orange slices for 2 minutes, then transfer the slices to an ice bath and discard the boiled water. This helps remove some of the bitterness of the peel and pith.
In the same large pot, bring 6 cups of water and 3 cups of granulated sugar to a boil. Add the orange slices, then reduce heat to low and simmer for 45-60 minutes, stirring occasionally to ensure the slices are evenly coated in the liquid. After simmering, the rinds should look slightly translucent.
Using a slotted spoon or spatula, remove the oranges from the liquid and spread evenly on a drying rack (see notes below if using a dehydrator or drying in the oven). Allow the slices to dry at room temperature for about 18 hours, flipping occasionally. The oranges will feel sticky, but not wet, when they're ready for the sugar coating.
If you'd like to keep the liquid (it's now orange simple syrup, which is great for cocktails), let it cool fully, then strain and transfer to an airtight container or bottle. Store in the fridge for up to three weeks.
After the orange slices have dried, gently toss them in ½ cup granulated sugar to coat (see notes below for Chocolate Drizzled Orange Slices variation). Serve immediately or store in an airtight container in the fridge for up to one month.