Melt butter in a saucepan over low heat. Stir in jasmine tea; heat for 5 minutes. Remove from heat and let stand for 5 minutes. Strain into a large bowl and discard solids. Let butter cool to room temperature, 20 to 30 minutes.

Preheat the oven to 350 degrees F (175 degrees C). Line a 9x5-inch loaf pan with parchment paper, leaving an overhang on 2 sides.

Whisk flour, baking powder, and salt together in a small bowl. Whisk sour cream and buttermilk together in a separate small bowl.

Add 3/4 cup plus 2 tablespoons sugar to the butter and beat with an electric mixer until light and fluffy, 3 to 4 minutes. Add eggs one at a time, beating well after each addition. Scrape down sides of the bowl and stir in almond extract.

Add the flour mixture in 3 additions, alternating with the sour cream mixture. Beat batter just until combined. Scrape batter into the prepared pan and sprinkle sliced almonds over the top.

Bake in the preheated oven until golden brown and a toothpick inserted into the center comes out clean, about 50 minutes. Tent loaf with foil if it starts to brown too quickly.

Transfer the pan to a wire rack and let cake cool for 15 minutes. Gently lift out loaf using the parchment overhang. Transfer to the rack and let cool completely before slicing.