Pour 1/2 cup (70 g) whole black sesame seeds into a dry 8-inch heavy-bottomed nonstick saucepan over medium-low heat and toast, stirring constantly with a heatproof silicone spatula, for 3 minutes until fragrant and popping slightly. Transfer 2 tablespoons (18 g) toasted seeds to a small shallow bowl for rolling, pulse the remaining 6 tablespoons (52 g) in a food processor for 20 seconds into a coarse, sandy meal, then melt 7 tablespoons (99 g) unsalted butter in the same saucepan over medium heat for 3 to 4 minutes until foaming with nutty golden-brown milk solids and pour into a wide ceramic mixing bowl to cool for 10 minutes.

Whisk 1/2 cup (60 g) sweet glutinous rice flour (mochiko), 2 tablespoons (25 g) granulated white sugar, and 1/2 cup (120 ml) whole milk in the wiped-out 8-inch nonstick saucepan until lump-free, then cook over medium-low heat while stirring continuously for 3 to 4 minutes until the mixture thickens into a glossy, translucent, stretchy dough that pulls cleanly away from the pan. Fold in 1 tablespoon (14 g) melted unsalted butter until fully absorbed and shiny, transfer the mochi onto a sheet of parchment paper to cool for 10 minutes, and divide into 12 equal 15-gram balls.

Whisk 2/3 cup (135 g) packed dark brown sugar and the remaining 2 tablespoons (25 g) granulated white sugar into the warm browned butter in the wide ceramic mixing bowl for 1 minute until glossy, then whisk in 1 room-temperature large egg (50 g) and 1 teaspoon (5 ml) pure vanilla extract until smooth and pale. Add the 6 tablespoons (52 g) ground black sesame meal, 1 1/4 cups (150 g) spooned-and-leveled all-purpose flour, 1/2 teaspoon (2.5 g) baking soda, and 1/2 teaspoon (3 g) fine sea salt, folding gently with the spatula just until a cohesive charcoal-grey dough forms with zero dry flour streaks.

Scoop the black sesame cookie dough into 12 equal portions (about 38 g each), flatten each portion between your palms into a 3-inch (7.5 cm) round disc, and press 1 cooled 15-gram mochi ball into the center. Bring the dark sesame dough edges up around the white mochi core, pinch the seam tightly closed, roll each stuffed ball in the reserved 2 tablespoons (18 g) whole toasted black sesame seeds, and chill on an 18x13-inch parchment-lined aluminum half-sheet pan in the freezer for 10 minutes while preheating the oven to 350°F (177°C).

Press each chilled dough ball gently with the palm of your hand into a 1/2-inch (1.2 cm) thick puck spaced 2 inches apart on the parchment-lined sheet pan, then bake on the center oven rack at 350°F (177°C) for 11 to 12 minutes until the edges are set and the tops develop delicate surface cracks around the sesame crust. Cool the cookies directly on the hot baking sheet for 10 minutes so the delicate crumb firms up around the molten mochi center, then transfer to a wire cooling rack and serve warm.