Preheat the oven to 400 degrees F. Line a large baking sheet with parchment paper.
Slice 1 cup of the strawberries and transfer to a small bowl. Add the lemon zest and mix well. Set aside.
Halve or quarter the remaining strawberries and transfer to a medium bowl. Add 2 tablespoons of the sugar, the lemon juice and a pinch each of salt and pepper; mix well. Let stand until juicy, stirring occasionally.
Meanwhile, in a liquid measuring cup or small bowl, whisk 1/2 cup of the heavy cream with the sour cream until just smooth. Set aside.
In a large bowl, whisk the flour with the 1/4 cup sugar, the baking powder, baking soda, and 1/2 teaspoon salt. Working over the bowl, grate the butter on the large holes of a box grater. Gently toss the butter with the dry ingredients, then stir in the sliced strawberries. Pour in the cream mixture and stir together until evenly moistened.
Scrape the mixture onto a work surface and fold a few times until the dough comes together, then pat into a 2-inch-thick rectangle. Using a knife or bench scraper, cut the dough into 6 equal scones. Transfer to the prepared baking sheet and sprinkle each scone with sugar. Bake until puffed and golden, about 30 minutes. Let cool.
Meanwhile, in another large bowl, whip the remaining 3/4 cup heavy cream with a whisk or electric mixer until stiff. Split the scones horizontally and fill with the whipped cream and juicy strawberries.