For the strawberry twists: Preheat the oven to 400 degrees F. Line two baking sheets with parchment paper.
Dust a work surface lightly with flour and then roll the puff pastry into a 12-by-14-inch rectangle. Rotate the rolled dough so the 12-inch side is parallel to you. Cut the dough in half horizontally by measuring 7 inches up the side, marking it there, and then cutting it in half using the mark as a guide. Evenly spread the strawberry jam over the bottom half of the dough, making sure to spread all the way to the edges. Dust the Strawberry Sugar over the jam. Top with the other half of the dough, pressing down lightly to adhere the top piece to the jam. Cut the dough into 1/2-inch strips using a pizza cutter, making about 24 strips. Twist each strip four or five times and then pinch the ends to prevent the twists from unraveling during baking. Place 12 strips onto each of the prepared baking sheets. Bake for 12 to 15 minutes, until golden brown. Remove from oven and let cool 5 minutes.
Use an offset spatula to release the twists from the parchment if any jam has leaked out. Let sit until cooled completely. Serve immediately or store in an airtight container for up to 1 day. (Makes 24 twists.)
For the strawberry whipped cream: Using a stand mixer fitted with the whisk attachment, whip the cream and Strawberry Sugar on medium-high speed until soft peaks form. Refrigerate for up to 2 hours before serving.
For the strawberry milkshake: Remove 6 strawberries from the quart and reserve for garnish. Remove the tops from the remaining strawberries. Cut approximately 4 strawberries lengthwise into 6 slices each, so you have 24 slices, and then roughly chop the remaining strawberries. Reserve for later use.
Pour some of the Strawberry Sugar into a small dish. Dip the rims of six 8-ounce glasses in water and then directly in the sugar. Carefully drop 4 slices of strawberries into the bottom of each glass. Use a skewer or offset spatula to press the strawberries up against the sides of the glasses so that when you pour the shake into the glass you will see the strawberries in the bottom of the glass. Hold the glasses at room temperature while you make the shake.
Place the chopped strawberries in a blender with the milk and strawberry jam. Mix on high speed until the strawberries break down into very small pieces. Add the softened strawberry ice cream and mix until blended.
Pour the shake into the prepared glasses; top with whipped cream. Serve with 2 twists and garnish with a whole strawberry by cutting a small slit in the bottom of the strawberry and resting it on the rim. Serve immediately.
Place the freeze-dried strawberries, sugar and cinnamon in a food processor and process until finely ground and blended; the sugar should be as fine as bartender's sugar. Store in an airtight container until ready to serve.
You can make the strawberry twists ahead of time and freeze them in a zip-top bag. When ready to serve, thaw the twists completely and then warm them up in the oven.