Special equipment: a large nonstick madeleine pan
Preheat the oven to 375 degrees F.
Melt the butter with the safflower petals in a small saucepan over a low flame. Set aside to cool slightly. In a small bowl whisk together the flour, baking powder and salt.
In a stand mixer fitted with a whisk attachment, whip the sugar and eggs until light yellow and thick, about 3 minutes. Add the orange zest and vanilla and mix until combined, about 30 seconds. Remove the bowl from the stand mixer and use a spatula to fold in first the flour mixture and then the safflower butter.
Fill the cups of a madeleine pan with batter and bake until golden, humped and springy, 12 to 13 minutes. Let cool for 5 minutes before unmolding the madeleines. Dust with confectioners' sugar prior to serving.