Move an oven rack to the middle position and turn the oven on to 325°F. Prepare a 9-inch round baking pan by lining the bottom with parchment paper and generously greasing the sides with butter or canola oil. Set aside.
Whisk together 1 ¼ cups all-purpose flour, 2 teaspoons baking powder, ½ teaspoon baking soda, and ½ teaspoon table salt in a medium bowl. Set aside for now.
In a separate small bowl or large measuring cup, whisk together 4 large eggs, ¼ cup canola oil, and ¼ cup plain or honey-flavored Greek yogurt. Set aside.
Add ½ cup honey and ¼ cup softened unsalted butter to a large bowl or the bowl of your stand mixer (fit it with a paddle attachment if using). Cream the honey and butter together on medium speed until it appears pale yellow and fluffy. Scrape down the sides of the bowl with a spatula.
Add half of the dry ingredients to the bowl with the creamed honey butter. Mix on low speed until all of the flour is incorporated. Scrape down the sides of the bowl, then add half of the egg mixture. Mix on high speed until evenly mixed. Scrape down the sides of the bowl, then repeat this procedure again with the remaining flour mixture and egg mixture.
Pour the batter into the prepared pan and smooth the top of the batter with a spatula. Bake for about 45 minutes until a toothpick inserted into the center of the cake comes out with crumbs clinging to it.
Honey Rose Syrup
While the cake is cooking, make the honey rose syrup. Add ½ cup honey and ¼ cup water to a small saucepan. Heat over medium heat and stir until the honey melts and mixes with the water to a syrupy consistency. Turn off the heat. Stir in ¼ cup rose water. Cover the saucepan to keep warm until the cake comes out of the oven.
While the cake is still warm and in the pan, poke holes all over the top of the cake with a toothpick or skewer. You don't want the holes to be too large, so don't use anything larger, like a chopstick.
Very slowly pour the honey rose syrup all over the top of the cake. If at any point you notice that the syrup is not sinking in, but pooling on the top, stop pouring and wait a couple of minutes for the syrup to absorb. Use all of the syrup.
Let the cake cool/rest for at least 30 minutes in the pan before removing it from the pan. To do this, carefully run a paring knife around the edges of the cake to loosen it. Place a large plate or platter over the cake pan, then carefully invert the cake pan over the plate. The cake should just fall out of the pan onto the plate. If not, tap the pan a few times to loosen it.
Serve the cake at room temperature or slightly warm. It can certainly be served as it is, but feel free to dress it up with some rose petals (make sure they haven't been sprayed with anything) or other edible flowers, or Greek yogurt, ice cream, fresh fruit or fruit compote, or a drizzle of liquid honey.
Notes
Don't use a smaller pan size here, or the batter will overflow. Alternatively, you can use an 8x8-inch square pan.