Bring the strawberry jam to a gentle simmer in a small saucepan, stir in the cornstarch whisked with water in a separate bowl, and cook for 3 to 4 minutes with occasional stirring before transferring the filling to a bowl. The slurry initially makes the jam cloudy, but the cooked mixture should become glossy and translucent as it thickens.
Beat the butter and sugar with the stand mixer’s paddle for 3 to 5 minutes, incorporate the whole egg and extra yolk thoroughly, then blend in the sour cream and vanilla. The creamed butter should look lighter and fluffy before the eggs go in, and the finished wet mixture should look evenly combined.
Whisk the flour, dough cornstarch, baking powder, baking soda, and salt in a large separate bowl, then feed this mixture gradually into the mixer on low speed. Stop as soon as the flour disappears so the dough stays tender rather than becoming overworked.
Cover the dough and refrigerate it for at least 1 hour or overnight, then put the cooled filling into a piping bag fitted with a small round tip and keep it chilled until shaping. The dough should feel firm enough to flatten and lift, while the filling should hold a mound rather than run across the dough.
Portion the dough into 2 tablespoonfuls, press each portion into a 3-inch disc with a shallow center, pipe in 1 to 2 teaspoons of filling, lift and pinch the edges closed, then place each pouch seam down on two parchment-lined 15x10x1-inch baking sheets at least 2 inches apart and refrigerate for at least 15 minutes. Each sealed cookie should completely surround the jam without an open seam or a visibly thin patch.
Heat the oven to 350°F, bake the chilled cookies for 10 to 12 minutes, and remove the sheets promptly when the cookies are done, leaving them on the sheets for 10 minutes to cool. Look for lightly golden edges and pale centers that appear set, rather than waiting for the entire cookie to brown.
Whisk the confectioners’ sugar with the milk until smooth, spread 2 teaspoons of icing over each cookie with a spoon back or offset spatula, immediately add a generous pinch of rainbow sanding sugar, and leave the topping to set for 10 minutes. The icing should form an even layer, with the sanding sugar clinging to its still-wet surface.