Trim ½-inch from the top and bottom of orange till the flesh is visible.
Place the flat end on a cutting board. With a sharp knife, slice off the peel and pith in sections, following the curve of the orange. At this point, the flesh will be fully exposed.
Working over a bowl, (you want to catch that beautiful juice!) hold the fruit in your hand, and cut between the white membranes to slice out each segment. Slice and rotate the orange.
Arrange segments on a platter. Pour the reserved juice from the bowl on top of segmented oranges in the platter.
Scatter with medjool date slivers, sea salt, slivered almonds, and dill.
Drizzle olive oil on top.