For saffron caramel pastry cream: In a medium pot, combine half and half, caramel squares, and Saffron Salt. Bring to a low simmer and stir often until caramels are completely melted and dissolved. Meanwhile, whisk together sugar, corn starch, and egg yolks in a medium bowl. When caramel cream is smooth, slowly drizzle the hot liquid into the yolk mixture while whisking constantly. Pour the combined mixture back into the pot and cook over medium heat, stirring constantly, until mixture is thick (about the consistency of pudding). Stir in vanilla extract. Pass cream through a fine sieve into a bowl and lay plastic wrap directly on the top of the pastry cream to prevent a skin from forming. Chill for at least 1 hour before using.
For beignets: Stir together warm water, sugar, and yeast in a large bowl. Let sit for 5 min., or until foamy. Add buttermilk, half and half, egg, salt, and baking soda. Add 2 1/2 cups of flour and stir until a shaggy dough forms, then add in butter pieces. Continue adding flour, 1/4 cup at a time, until butter is incorporated and the dough is no longer sticky. Transfer onto a lightly floured surface and knead until dough is smooth and soft, about 5 to 6 min. Place in a lightly oiled bowl and let proof for about an hour, or until the dough has doubled in size. Turn proofed dough back out onto a floured surface and roll out to a 1/2-inch thickness. Cut into 2 1/2-inch squares and lay onto a floured baking sheet to proof again for 25 to 30 min., or until beignets have puffed up slightly. Pour about 3 inches of oil into a large pot and heat to 375 degrees. Gently lower a few beignets at a time into the oil and fry for 2 min. per side, or until golden brown. Place fresh beignets on a baking sheet lined with paper towels or a wire rack to drain excess oil.
To fill: Spoon pastry cream into a squeeze bottle or a bag with a round piping tip. Use a chopstick or thick skewer to poke a hole in the side of each beignet. Wiggle the chopstick a little to create more room on the inside of the beignet, but don't pierce through any other sides. Place tip of squeeze bottle/piping tip into the beignet and slowly squeeze to fill each one with about 1 Tbsp. of cream. Dust filled beignets generously with powdered sugar before serving.