Preheat the oven to 325°F (163°C). Line two baking sheets with parchment paper.
In a large bowl, cream the softened butter and granulated sugar together using an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add the vanilla extract and mix until combined.
In a separate bowl, whisk together the all-purpose flour and salt.
Gradually add the flour mixture to the butter mixture, mixing on low speed until the dough just comes together. Do not overmix.
Turn the dough out onto a lightly floured surface and gently knead it a few times to bring it together.
Roll the dough out to about 1/4 inch thickness.
Use a 2-inch round cookie cutter to cut out cookies and place them on the prepared baking sheets about 1 inch apart.
Press one edible flower petal gently onto the top of each cookie, lightly pressing it into the dough so it adheres.
Bake the cookies in the preheated oven for 20-25 minutes, or until the edges are just beginning to turn golden.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.