Preheat the oven to 325°F (165°C). Line two baking sheets with parchment paper.
In a large mixing bowl, cream the softened unsalted butter and granulated sugar together using an electric mixer on medium speed until light and fluffy, about 3 to 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 (6 mm) thickness.
Use a 2-inch (5 cm) round cookie cutter to cut out cookies and place them on the prepared baking sheets about 1 inch apart.
Gently press one edible flower petal onto the top center of each cookie, pressing lightly so it adheres to the dough.
Bake the cookies in the preheated oven for 18 to 20 minutes, or until the edges are lightly 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.
Store the cooled cookies in an airtight container at room temperature for up to 5 days.