Preheat the oven to 425°F. Drizzle the oil into the cake pan and, using paper towels, rub it all over the bottom and sides of the pan. Set aside. Toast the almonds. Place the almonds in a small, dry skillet over moderate heat. Shake the pan regularly until the nuts are fragrant and evenly toasted, about 2 minutes. Watch carefully! They can burn quickly. Transfer the nuts to a large plate to cool. Set aside.
In a food processor or a blender, combine the sugar and almonds and chop until fairly fine. Add the flour, baking powder and salt and blend. Transfer the mixture to a large bowl. Add the eggs and stir to blend. Add the Carrots and stir to blend. The batter will be fairly thick but should not be dry. Transfer the batter to the prepared pan. Smooth out the top with a spatula. Place the pan in the center of the oven and bake until golden and firm and a toothpick inserted into the center of the cake comes out clean, 40 to 45 minutes. Transfer to a rack to cool. After 10 minutes, run a knife around the edges of the pan. Release and remove the side of the springform pan, leaving the cake on the pan base.
While the cake cools, prepare the sauce: combine the lemon juice and sugar in a small saucepan and simmer over low heat until the sugar is dissolved, 2 to 3 minutes. Serve the cake at room temperature: cut it into thin wedges and top with the warm lemon sauce and a scoop of sorbet. The cake should be served the same day it is baked. Serves 16.
Lemon Thyme Sorbet
In a large saucepan, combine the sugar, Thyme and 2 cups of water and bring to boil over high heat. Remove from heat, cover and set aside to steep for 1 hour.
Strain through a fine-mesh sieve, discarding the thyme leaves. Stir in the lemon juice and zest. Cover and refrigerate until thoroughly chilled. Transfer to an ice-cream maker and freeze according to the manufacturer's instructions. The sorbet should be served as soon as it is made.