Line 3-4 baking sheets with parchment paper or silicone mats. Set aside.
Make the dough: In a medium sized bowl, place 3 cups of flour. With a pastry cutter, cut in the cold, sliced butter until large pea sized balls form, with larger chunks visible. Place the bowl in the fridge.
In the bowl of a stand mixer, add the remaining 2 cups flour and yeast; whisk to combine.
In a saucepan or microwave-safe dish, heat the half and half, sugar and salt to between 120 and 130°F. Add to yeast and flour mixture in stand mixer bowl. Add egg. Using a paddle attachment, beat until combined.
Add the cold flour and butter mixture; mix until combined. The dough will look kind of craggy at this point.
On a well floured surface, turn out the dough and knead a few times. Form into a rough square shape. Roll the dough into a 21x12-inch rectangle. Starting with the short side, fold dough into thirds, forming a 12x7-inch rectangle.
Give the dough a quarter turn and roll into a 21x12-inch rectangle. Fold the dough into thirds, starting with the short side.
Repeat for a third time - give the dough a quarter turn and roll into a 21x12-inch rectangle. Fold the dough into thirds, starting with the shorter side. You will end up with a 12x7-inch rectangle.
Place the dough that is now folded into thirds, on a parchment lined baking sheet. Cover and place in the fridge for 4 hours.
Make the filling: In the bowl of your stand mixer, mix the softened butter and confectioners' sugar until combined. Break off pieces of the almond paste and add to the mixer. Mix until smooth. Add the 2 egg whites, all-purpose flour and almond flour or finely chopped almonds. Combine until a smooth paste forms. Place in the fridge until you are ready to fill the pastry.
Take the cold dough out of the fridge and lightly flour your work surface. Let the dough stand for about 5 minutes before you attempt to roll it out.
Cut the dough in half width-wise. You will have two 6x7-inch pieces. Roll each portion into a 12-inch square and set one aside.
For the smaller Bear Claws: Cut the first square into three 12x4-inch strips. Spread about 3 heaping tablespoons of the filling down the middle of the each of the strips. Fold the long edges together over the filling. Press the edges and ends to seal. Cut into three equal pieces. Seal each end of the cut pieces as well, so the filling doesn’t spill out. With the seam side facing away, cut 4 equally spaced slits about ½-inch long. Slightly bow out (curve) the pastry. Place up to 8 bear claws on each lined baking sheet. Repeat with 2nd dough square. Cover and let rise in a warm place for 1 hour.
For the larger Bear Paws: Cut the first square of dough in half. Fill the dough down the middle lengthwise with 8 heaping tablespoons of filling. Fold the long edges together over the filling. Press the ends and edges to seal. Cut into three equal pieces. With the seam side facing away, cut 4 equally spaced slits about ½-inch long. Slightly bow out (curve) the pastry. Place 3 pastries per lined baking sheet. Let rise in a warm place for 1 hour.
Preheat oven to 375°F.
In a small bowl, beat an egg white until foamy. Brush the tops of each pastry with the egg white. Sprinkle liberally with the Turbindo sugar. Sprinkle tops with sliced almonds.
Bake smaller bear claws for 14 to 15 minutes or until golden brown.Bake larger bear paws for 22 to 34 minutes or until golden brown.
Make the glaze: Whisk the confectioners' sugar and half and half until smooth and creamy. You may add more or less half and half until you reach the desired consistency.
Remove the pastries from the baking pans and place on wire racks with wax paper underneath. Make sure the pastries are cool before you drizzle them with the glaze.
If you have any leftover pastries, wrap each individually in wax paper and foil, then freeze for up to a month. You can microwave them for about 20 seconds to warm them up nicely before devouring them.