Step 1

Finely grind star anise, cinnamon, cardamom, cloves, rose petals, fennel seeds, nutmeg, peppercorns, and saffron in spice mill to a powder. Transfer spice mixture to a small bowl.

Step 2

Working in batches if needed, finely grind almonds, poppy seeds, cashews, and pistachios in spice mill (but not so finely ground that the nuts turn to butter). Whisk nut mixture into spice mixture until well combined.Do Ahead: Thandai masala can be made 3 weeks ahead. Transfer to an airtight container; cover and chill.

Step 3

Using an electric mixer on medium speed, beat butter, sugar, and vanilla in a large bowl until light and creamy, about 3 minutes. Add flour, salt, and 5 Tbsp. (35 g) thandai masala and beat on low speed until just combined. Pat dough into a disk and wrap tightly in plastic. Chill until firm, at least 2 hours.

Step 4

Place racks in upper and lower thirds of oven; preheat to 350°. Roll out dough between 2 sheets of parchment paper to ¼" thick. Transfer dough, still sandwiched between parchment, to a baking sheet and freeze until just firm, 10–15 minutes.

Step 5

Slide dough onto a surface and carefully peel away top sheet of parchment. Punch out cookies as close together as possible with cutter and divide between 2 parchment-lined baking sheets, spacing 1½" apart.

Step 6

Bake cookies, rotating baking sheets top to bottom and front to back halfway through, until golden, 14–16 minutes. Let cool 5 minutes on baking sheets, then transfer to a wire rack and let cool completely; reserve baking sheets with parchment. Repeat process with dough scraps (chill dough again before punching out more cookies).

Step 7

Melt white chocolate and oil in a small heatproof bowl set over a small saucepan of barely simmering water (do not let bowl touch water), stirring occasionally, until glossy and smooth. (Alternatively, melt in a microwave-safe bowl in the microwave in 20-second increments, stirring after each, about 1 minute total.)

Step 8

Dip one third of each cookie into white chocolate and transfer to reserved baking sheets. Scatter pistachios and rose petals over white chocolate. Freeze cookies until chocolate is set, about 5 minutes.Do ahead: Dough can be made 1 week ahead; keep chilled. Cookies can be baked (but not glazed) 10 days ahead or glazed 2 days ahead; store airtight at room temperature.