The pastry dough -- Put the flour, sugar, and salt in the bowl of a food processor. Process for just 2 seconds. Add the butter, and then pulse the machine about 5 times, until the butter becomes crumbly. Beat the egg in a glass measuring cup, and then add enough heavy cream to equal one-half cup. Gradually add up to one-third of the egg mixture to the flour mixture, pulsing the machine until a clumpy dough develops. Put the remaining egg mixture in the refrigerator -- it will later be brushed onto the dough.
Turn the dough onto a non-floured work surface. Form the dough into a rough ball, and then flatten the ball to make a disk. Wrap the disk in cling film and refrigerate for 1-2 hours (or for up to 3 days).
Rolling out the dough -- On a lightly floured surface or pastry cloth, roll the dough into a 12-inch-diameter circle. Transfer the dough to a parchment lined baking sheet, and then put the sheet in the refrigerator while you prepare the strawberry filling.
The strawberry filling -- In a medium or large bowl, whisk together the cornstarch and sugar. Hull the strawberries, and then cut them in lengthwise in half. (Cut large berries into thirds.) Put the berries in the cornstarch mixture, and gently toss with a spatula until all are coated. Let the berries macerate (exude their juices) for at least 15 minutes.
Assembling, forming, and brushing the galette -- Preheat the oven to 400°F. While the oven is heating, put up to 1 tablespoon of cornstarch on the center of the dough, and then spread it out, with your fingers, to within 1 1/2 inches from the edge. Spread the strawberries and their now-thickened juices on top of the cornstarch. Fold the edge of the dough over the outermost berries, making pleats as you go. Brush the remaining egg-and-cream mixture onto the exposed dough. If desired, sprinkle the brushed dough with a teaspoon or two of sugar.
Baking and serving the galette -- Bake in the preheated oven until the crust browns and the juices bubble -- 40-45 minutes. Let cool for 5-10 minutes on the baking sheet. Then transfer the galette on its parchment paper to a wire rack. When cool enough to handle, slide the galette onto a cutting board for easy slicing. Enjoy with or without whipped cream, ice cream, mascarpone, or creme fraiche.