Cake
Nonstick vegetable oil spray or unsalted butter, room temperature (for pan)
1¾ cups (219 g) all-purpose flour
1½ tsp. baking powder
¾ tsp. baking soda
¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt
½ cup sour cream, room temperature
½ cup whole milk, room temperature
¾ cup (150 g) granulated sugar
½ cup (1 stick) unsalted butter, room temperature
2 Tbsp. vegetable oil
1 tsp. vanilla extract
½ tsp. almond extract
2 large eggs, room temperature
¼ cup Thandai Masala
Filling and assembly
8 oz. cream cheese, room temperature
½ cup (or more) whole milk, room temperature, divided
5 Tbsp. powdered sugar, divided
½ tsp. almond extract
1 Tbsp. Thandai Masala
1 cup chilled heavy cream
Cake
Step 1
Place a rack in middle of oven; preheat to 350°. Line bottom of an 8x8" baking pan with a square of parchment paper (no need to leave any overhang). Lightly coat parchment and sides of pan with nonstick vegetable oil spray or unsalted butter, room temperature. Whisk 1¾ cups (219 g) all-purpose flour, 1½ tsp. baking powder, ¾ tsp. baking soda, and ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a medium bowl to combine.
Step 2
Whisk ½ cup sour cream, room temperature, and ½ cup whole milk, room temperature, in a small bowl until smooth.
Step 3
Using an electric mixer on medium speed, beat ¾ cup (150 g) granulated sugar and ½ cup (1 stick) unsalted butter, room temperature, in a large bowl until well combined, about 2 minutes. Scrape down sides of bowl with a rubber spatula, then add 2 Tbsp. vegetable oil, 1 tsp. vanilla extract, and ½ tsp. almond extract and beat until just combined. Add 2 large eggs, room temperature, one at a time, beating until incorporated after each addition, about 2 minutes total. Reduce speed to low and add dry ingredients in 3 additions, alternating with sour cream mixture in 2 additions, starting and ending with dry ingredients and scraping down sides of bowl halfway through. Beat until just combined (be careful not to overmix). Sprinkle ¼ cup Thandai Masala over and fold in with a rubber spatula just until incorporated.
Step 4
Scrape batter into prepared pan and smooth surface with an offset spatula. Bake cake until golden brown, top springs back when gently pressed, and a tester inserted into the center comes out clean, 30–35 minutes. Transfer pan to a wire rack and let cake cool in pan, about 1 hour.
Filling and assembly
Step 5
While the cake is cooling, using electric mixer with clean beaters on medium-high speed, beat 8 oz. cream cheese, room temperature, until very smooth, about 2 minutes. Reduce speed to medium-low and beat in ¼ cup whole milk, room temperature. Scrape down sides of bowl, reduce speed to low, and beat in 3 Tbsp. powdered sugar and ½ tsp. almond extract until just combined, about 1 minute. Increase speed to medium and beat until very smooth, about 2 minutes. Scrape down sides of bowl and add remaining ¼ cup whole milk, room temperature, and beat until combined. Mixture should be the consistency of whole milk yogurt; if it’s much thicker, beat in more milk, 1 Tbsp. at a time, until the right consistency. Beat in 1 Tbsp. Thandai Masala. Transfer ⅓ cup filling to a small bowl; cover and chill until ready to assemble cake.
Step 6
Using the handle of a wooden spoon, poke holes over entire surface of cooled cake, spacing 1" apart and going all the way through to the bottom. Gradually pour remaining filling over cake, making sure to pour into holes. (There will be some filling sitting on top.) Chill cake until filling is set, at least 1 hour.
Step 7
Using electric mixer on medium speed, beat 1 cup chilled heavy cream, remaining 2 Tbsp. powdered sugar, and reserved ⅓ cup chilled filling in a large bowl until stiff peaks form (be careful not to overbeat).
Step 8
Dollop whipped cream mixture over cake. Using a spoon, swirl decoratively over entire surface, or, using offset spatula, spread into an even layer. Cut cake into squares to serve.