Preheat the oven to 350ºF (180ºC). Line two large baking sheets with parchment paper
In a large bowl, beat the butter, with an electric mixer on medium speed, until smooth. Add the rose petals and beat on low speed until combined.
Add the powdered sugar, vanilla extract and salt. Beat until well combined.
On low speed, mix in the flour in two additions. Beat just until combined.
Roll the dough into 1 1/4-inch balls, about 1/2 ounce (14g) each. Place the dough balls about 2 inches apart onto the prepared baking sheets.
Bake for 7 minutes, then remove from the oven. Press indentations into each cookie with a 1-inch diameter pastry tamper or with the flat top of a 1-inch diameter bottle cap.
Return the cookies to the oven and continue baking until the edges are light golden brown, about 5-6 more minutes.
If the indentations in your cookies lose definition, press again with the tamper or bottle cap while the cookies are still hot on the baking sheet.
Transfer the cookies to a cooling rack to cool completely.
Filling
In a small saucepan, bring the pureéd raspberries to a simmer over medium heat. Simmer until the purée is reduced by half, about 5 minutes. Transfer the raspberry reduction to a small bowl and set aside.
Place the white chocolate in a medium heat safe bowl and set aside.
In a small saucepan over medium heat, bring the heavy cream to a simmer, just until bubbles form around the edges. Do not boil. Stir in the raspberry reduction and heat just to a simmer again. Do not boil.
Pour the hot cream mixture over the white chocolate, making sure all of the white chocolate is submerged. Let it sit for 2 minutes, then stir with a spatula until smooth.
Let the ganache cool until slightly thickened. Spoon about 1/2 teaspoon into the indentation of each cookie. The ganache will continue to firm up as it sits.
When the ganache in the cookies has firmed up, decorate with dried rosebud or rose petals, if desired.