Preheat oven to 375 degrees F, with the center rack in place and a piece of aluminum foil on the bottom rack to catch any oils that might seep out of the pan. Lightly butter a 10-inch removable-bottom tart pan.

In a medium bowl, combine diced rhubarb, sugar, cardamom, rose petals, and rose water. Let sit for 10–15 minutes, until juices begin to form, while you make the pastry dough.

Combine flour, sugar, baking powder, salt, and butter in a food processor. Pulse to cut the butter into dry ingredients; the mixture will be the consistency of coarse sand. Pour into a medium bowl. Add gently beaten egg and egg yolks. With a fork, mix until the egg is evenly distributed and pastry dough clumps together. Gather pastry dough with your hands and press it evenly onto the bottom—but not up the sides—of the prepared tart pan.

Use your hands to evenly distribute the rhubarb mix onto the tart starting from the center, out to ¾ inches from the edge, leaving the juices behind. The edges must remain clear so the dough can rise.

Place the tart pan on the center rack; bake for 50–55 minutes, until pastry is a dark, golden brown at the edge.

Let cool for 10 minutes and remove the rim of the tart pan; doing so while it’s still warm helps keep it from sticking. Let tart cool and serve at room temperature.