Heat the oven to 157°C with racks in the upper and lower thirds.

Make the cookie dough: In a stand mixer, cream the butter and both sugars together on medium speed until fluffy and light in colour for about 5 minutes
Scrape down the bowl halfway through.

Combine the flour, baking powder, baking soda, matcha, and salt in a medium bowl and set aside.

Add the eggs and vanilla to the sugar mixture and mix until well combined. Add the flour mixture to the sugar mixture and mix on low speed until just combined, about 1 minute.

Scrape down the sides of the bowl with a spatula and form the dough into a round disk. At this stage, the dough shouldn't be sticky. Wrap the dough in plastic wrap and transfer to the refrigerator to chill for up to 20 minutes.

Make the raspberry mochi: In a medium microwave-safe bowl, thoroughly mix the rice flour, cornstarch, sugar, milk, salt, and raspberry preserves with a spoon. Microwave the mixture for 1 minute on high. Stir the mixture. Repeat this process 3 more times for a total of 4 minutes, using a towel or oven mitt to hold the bowl, as it will get hot. The mochi should be thick. Immediately stir in the butter and mix constantly, until the mixture is so elastic that when you pull the spoon out, it stretches instead of rips, about 2 minutes. If the mochi doesn’t stretch after 2 minutes, continue to mix until stretchy.

Fill a small bowl with the canola oil and pour a little from the bowl onto a plate to coat. Coat a small cookie scoop (a #60 or #70 scoop works best; or use a 1 tablespoon measuring spoon) with the oil as well. Scoop out the mochi and roll into little balls, then place on the greased plate.

Line two sheet trays with parchment paper. Remove the chilled dough from the refrigerator and scoop it into balls using a large cookie scoop (a #20 scoop works best; or scoop 3-tablespoon portions). Place each cookie dough ball on the prepared sheet pans.

Flatten each cookie dough ball into a round slightly larger than 3 inches in diameter and place a mochi ball in the center. Fold the dough over the mochi in half to enclose the mochi in a half-moon shape. Carefully roll the dough back into a ball, taking care not to rip the dough. Repeat with all the remaining cookie dough. If the dough gets too soft (and starts to stick to your hands), you can return it to the refrigerator for 15 minutes.

Place 6 cookies per sheet tray, leaving at least 3 inches of space between each cookie. Bake for 14 to 15 minutes, until the edges turn slightly golden.