Chop fresh strawberries and toss with 1 tablespoon of the sugar. It's not absolutely necessary, but you can cover and refrigerate for at least 30 mins for added flavor.
Heat oven to 375 degrees F.
In food processor, add flour, baking powder and soda, 4 tablespoons sugar. Pulse a few times to combine. Add butter to the mixture and pulse about 25 times, or until butter pieces are well-blended and very small.
Empty into bowl, add strawberries and combine.
Whisk cream with one egg until just blended; add vanilla extract. Starting with just 1/4 cup of the cream mixture, stir in the heavy cream (gently) until completely combined and dough holds together. If you need to add a little more heavy cream, in addition to the one cup of cream mixture, it's ok. Batter should be thick and slightly tacky. If the texture is crumbly, add a little more cream until it holds shape when gently squeezed.
Turn out onto floured surface, knead a couple times and shape into 8 inch circle, about 1 1/2 inches thick.
Slice like pie into 8 pieces and brush with egg wash. Dust with turbinado sugar.
Bake for about 25 minutes until tops are golden brown