Heat oven to 375 degrees F.
Chop fresh strawberries and toss with 1 tablespoon of the sugar. Cover and refrigerate for at least 30 minutes.
In food processor, add flour, baking powder and soda, 3 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; combine.
Whisk cream with one egg until just blended; add vanilla extract. Starting with just 1/4 cup of the cream mixture, stir in gently until completely combined and dough holds together. Batter should be thick and slightly tacky. If the texture is crumbly, add a little more cream until dough holds shape.
Turn out onto floured surface, knead a couple times and shape into an 8-inch circle. It should be about 2 inches thick.
Slice into 8 pieces (like a pie) and brush top surface with egg wash. Dust with Turbinado sugar.
Bake for about 25 minutes, or until tops are golden brown.