Preheat oven to 325 degrees. Butter a 10-by-15-inch rimmed baking sheet; line bottom with waxed paper. Butter paper; set aside. In a medium bowl, whisk together flour, baking powder, and salt; set aside.
In a mixing bowl, cream butter and sugar until light and fluffy. Add eggs one at a time, beating well after each, then beat in vanilla. With mixer on low speed, add flour mixture, and mix until just combined (batter will be as thick as cookie dough).
Spread batter evenly on prepared baking sheet; scatter cherries over the top. Bake cake until golden and a toothpick inserted in center comes out clean, 35 to 40 minutes. Cool 10 minutes in pan. Invert onto a wire rack; reinvert onto another rack to cool completely (top side up).
To serve, cut cake into triangles with a serrated knife. Dust with confectioners' sugar, if desired.
Sprinkle cherries over batter, which will puff up and around the fruit as it bakes.