Combine the sugar, 1/3 cup water and the kosher salt in a medium saucepan over medium heat, stirring just until the sugar dissolves. Cook, gently swirling the pan occasionally but not stirring, until amber, 8 to 10 minutes.
Brush any sugar crystals off the side of the pan with a wet pastry brush.
Remove from the heat and carefully whisk in the butter (the mixture will bubble).
Pour into a 9-inch-round cake pan, tilting the pan to coat the bottom; set aside.
Slice off the top and bottom of the oranges.
Place the oranges cut-side down and cut off the peel and white pith with a chef's knife, following the curve of the fruit.
Cut along both sides of each membrane to remove the segments. Set the segments aside, discarding any seeds.
Make the cake: Preheat the oven to 350 degrees F.
Spread the almonds on a baking sheet and roast until golden brown, 8 to 10 minutes.
Let cool, then transfer to a food processor and pulse until finely ground.
Transfer to a medium bowl; add the flour, baking powder, baking soda and kosher salt and whisk to combine.
Beat the butter and sugar in a large bowl with a mixer on medium-high speed until fluffy, about 5 minutes. Beat in the eggs one at a time, scraping down the bowl as needed. Beat in the orange zest. Reduce the mixer speed to low; beat in the flour mixture in 3 batches, alternating with the sour cream, beginning and ending with flour, until just smooth.
Arrange the orange segments in the cake pan in concentric circles.
Add the batter and smooth the top.
Bake until golden brown and a toothpick inserted into the center comes out clean, 40 to 45 minutes. (Tent with foil if the top gets too dark.)
Transfer to a rack and let cool slightly, then run a knife around the edge of the cake and invert onto a platter.
