Begin by preparing the pastry dough. Whisk the flour, sugar and salt together in a large bowl or food processor.
Cut in the butter with a pastry blender, your fingers or a food processor until the mixture resembles even, coarse sand without any larger pieces.
Next, add the ice water to the mixture and stir together with a fork until a dough forms. Use your hands to gather the dough into a rough ball. Divide the dough into two parts with one part larger than the other (1/3 and 2/3 sized portions respectively). Wrap each piece in plastic wrap or parchment paper and flatten into a small rectangle. Refrigerate until cold, about 2 hours or up to 2 days.
To prep for the filling, slice all the strawberries and rhubarb pieces and lay them out on a paper towel to absorb extra juices.
Once the dough has been chilled, it is time to begin assembling your strawberry galette cross! When ready to assemble, start by preheating the oven to 400℉.
Prepare the filling by tossing the strawberry slices and rhubarb slices with the granulated sugar, zest of half a lime and flour.
Roll out the larger piece of dough into a large rectangle on a slightly floured piece of parchment paper. On a separate piece of parchment, roll out the smaller piece of dough into a rectangle. Cut this smaller rectangle in half and attach each piece to the larger rectangle, one piece on each side to create the shape of a cross. Press the seams together.
Next, add the raspberry jam to a bowl and gently mix with a spoon to smooth. Spread the smoothed jam onto the dough cross, leaving a 1 ½" border bare along all the sides.
Layer the strawberry and rhubarb slices over the jam in 3 rows down the center and 2 rows on each side. Fold the edges of the pastry up and over the fruit and press it gently. If needed, you can cut diagonal slits in the inside corners of the cross to help the dough fold, however you will have less leakage as the galette cooks if you leave the dough intact.
Using the parchment paper, carefully transfer the galette to a rimmed baking sheet. Brush the edges with the beaten egg and sprinkle with the coarse sugar. Bake until the filling is bubbling and the crust is deep golden brown, about 40 to 50 minutes. Galettes always leak a little bit, so don't worry if the juices seep out onto the parchment!
Let the galette cool at room temperature for 15 minutes, then carefully use a long spatula to loosen the bottom of the crust from the parchment paper and slide it onto a serving plate. Serve warm or room temperature either plain or with a dollop of ice cream or whipped cream. Enjoy!