Stir together flour, cornmeal, baking powder, salt, and rosemary in a medium bowl. In a spouted measuring cup, whisk together together water and olive oil.
Make a well in the center of the dry ingredients and add oil and water gradually while stirring with a wooden spoon. Stir until dough forms. Knead dough gently 4 or 5 times.
Roll dough 1/8-inch thick on a well-floured surface. Cover with plastic wrap and let rest for 20 minutes.
Meanwhile, grease the wells of 24 standard-sized muffin cups. Dust with corn meal, swirling pan to allow it to stick to the sides of each well. Invert pans over the sink and tap the edge to remove excess cornmeal.
Using a 3 3/4-to 4-inch flower-shaped cookie cutter, stamp out as many flowers as possible. Gently transfer the dough to prepared muffin tins, tucking each flower gently into one of the cups. Gather the scraps, re-roll, and allow the dough to rest again before stamping out additional crackers.
With a toothpick or sharp skewer, prick holes in the dough on the bottom and up the sides of each cup, about 1/8 to 1/4 inch apart. Bake in an oven preheated to 450° F for about 10-12 minutes, until golden around the edges, shifting the baking sheets halfway through for even baking. Remove cracker cups with a thin metal spatula and cool on a rack. Fill as desired.