Combine the sugar, yeast, and water in the bowl of a stand mixer fitted with the dough hook. Let stand until foamy, about 5 minutes. Add the flour, salt, olive oil, canola oil, and egg yolks. Mix on low speed until the dough comes together and begins to pull away from the sides of the bowl, about 1 minute.
Gradually mix in the butter, mixing for another minute. Scrape down the side of the bowl and continue mixing for 2 more minutes. Cover the bowl and let the dough rise at room temperature until it has quadrupled in volume, about 4 hours.
Fill a large pot with a generous 2 inches of canola oil. Heat over medium heat until the oil registers 350°F on a candy thermometer. Line a baking sheet with paper towels.
Use an ice cream scoop to drop balls of dough into the hot oil, adjusting the heat as necessary to maintain the oil temperature. Fry the donuts in batches until golden, 4 to 6 minutes. Remove from the pot with a slotted spoon to drain on the prepared baking sheet. Let cool slightly.
MAKE THE ROSE PETAL SUGAR:
Combine the sugar and crushed rose petals in a shallow bowl.
Poke a hole in each donut with the tip of a paring knife. Spoon the jam into a large resealable plastic bag, press out the air, and twist the top until the bag feels tight. Snip off a corner of the bag and squeeze the jam into each donut until a bit oozes out. Roll the filled donuts in the rose petal sugar. Serve warm.