Preheat the oven to 350 degrees F (180 degrees C). Grease and line a 20-centimeter or 8-inch square baking pan with non-stick parchment paper.
In the bowl of a stand mixer fitted with the beater attachment, beat together the Unsalted Butter (1 cup) and Granulated Sugar (2/3 cup) on medium-speed until pale and fluffy, about 4 minutes. Pause mixing to scrape down the bottom and sides of the bowl.
Beat in the Vanilla Extract (1 teaspoon), Fresh Lemon Thyme Leaves (1 tablespoon), and Salt (1/2 teaspoon).
Add in the Fine Semolina Flour (100 gram) and All-Purpose Flour (175 gram) and beat until just combined, about 30 seconds.
Press the dough into the prepared baking tin, making sure to spread it into an even layer and to the edges of the pan. Sprinkle the Granulated Sugar (1 teaspoon) over the shortbread.
Bake, for 30 to 35 minutes, or until puffed, just firm, and lightly golden.
Remove from the oven and let the shortbread cool for 15 minutes in the pan before carefully transferring it out and onto a wire rack. Slice the shortbread into even squares while it is still warm.
Place the Fresh Blackberries (16 ounce) in a medium pot, along with the Granulated Sugar (1/2 cup), juice of the Lemon (1), and Vanilla Extract (1 teaspoon). Bring the berries to a simmer over medium heat, stirring occasionally, until the berries have completely broken down and are very soft, 15-18 minutes.
Strain the blackberry mixture into a bowl. You will need 1 cup of blackberry puree. If you have more than 1 cup, you can return the puree to the pot and bring it to a simmer. Simmer for 10-15 minutes to reduce it slightly to concentrate the flavors. Leave the puree to cool while you prepare the cream.
In the bowl of an electric mixer, beat the Heavy Cream (2 cup) and Powdered Confectioners Sugar (1 1/3 cup) to medium peaks, 3-4 minutes.
Add the Greek Yogurt (1 cup) to the whipped cream mixture and whisk until just combined. Reserve about 1 cup of the whipped cream yogurt mixture in a separate bowl.
Gently fold the blackberry puree into the whipped cream yogurt mixture.
Building the trifles is free form; you can do it in any order you like. I started with the blackberry yogurt mixture, followed by a layer of shortbread, another layer of blackberry yogurt and finally a bit of the plain yogurt cream on top with a garnish of shortbread and fresh blackberries.
Once all of your glasses are filled, freeze the trifles just until the top layer is firm. This should take about 30 minutes to 1 hour.
Once the trifles have chilled in the freezer after assembling, store them in the refrigerator if you are not going to eat them right away. Let the trifles sit at room temperature for 5 minutes before serving.