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Heat the oven to 350. Oil a 9-inch square baking pan and line it with parchment, leaving a 2-inch overhang on two sides.
In a large bowl, whisk together the oil and tahini. Add the egg, egg yolk and milk and whisk until completely smooth. Whisk in ¾ cup sugar and the vanilla.
Add the flour, baking powder and salt and fold in with a rubber spatula. Reserve about 2 tablespoons of the chocolate and add the remainder to the batter. Fold in 1 tablespoon sesame seeds.
Transfer the batter to the prepared pan. Sprinkle the reserved chocolate, the remaining ¼ cup sesame seeds and remaining 2 tablespoons sugar evenly over the top. Bake until the cake is puffed and set and a toothpick inserted into the center comes out almost clean with a few moist crumbs attached, 25 to 30 minutes. Let cool 10 minutes in the pan, then lift the cake out of the pan using the parchment overhang and transfer to a wire rack to cool completely.
To serve, cut the cooled cake into 16 pieces. Store leftovers in an airtight container for up to 3 days or freeze for up to 3 months. Thaw uncovered at room temperature before serving.