Preheat the oven to 350 degrees F. Spray a loaf pan with nonstick cooking spray.
Place a large nonstick skillet over medium-high heat. Add 2 tablespoons olive oil and heat until shimmering. Carefully pour in 2 cups of the grapes, being mindful that the oil may pop or splash. Add the thyme. Sprinkle the grapes with 2 tablespoons brown sugar and 1/2 teaspoon fine salt. Cook, stirring frequently, until the grapes soften and the sugar dissolves into a thin syrup, 6 to 8 minutes. Turn off the heat and cool the syrup in the skillet. Once cooled, remove and discard the thyme. The syrup will thicken as it cools.
Meanwhile, make the cake batter. Combine the cake flour, baking powder and the remaining teaspoon fine salt in a medium bowl. Add the granulated sugar, eggs and remaining 1/4 cup brown sugar into a stand mixer with a paddle attachment. Beat the egg mixture on medium speed until thickened and fluffy, 3 minutes. Add the almond extract. With the mixer running on low speed, slowly pour in the remaining 3/4 cup olive oil. Continue mixing until the olive oil is emulsified into the batter. Turn off the mixer and add half of the dry ingredients. Mix on low speed just until the ingredients are incorporated, scraping down the bowl as needed, then pour in the milk. Turn off the mixer and add the remaining dry ingredients. Mix on low speed just until the batter comes together, scraping down the bowl as needed.
Pour the batter into the prepared loaf pan. Stud the top of the cake with the remaining 1 cup grapes. Bake until the cake is golden brown and pulling away from the side of the pan, about 1 hour 40 minutes. The surface of the cake should look dry and slightly cracked.
Allow the cake to cool completely before removing from the pan. When ready to serve, garnish each slice of cake generously with the grape syrup.