Preheat a large saute pan over medium heat and melt the butter and olive oil together. Add the sliced onions, season with salt and pepper. Reduce the heat to medium-low and slowly cook the onions for about 1 hour (longer if desired), stirring occasionally until the onions are soft and caramelized. Set aside to cool.
Preheat the oven to 400 degrees F.
Cut one of the refrigerated pie crusts into a square (removing the rounded edges, discarding or saving for later use), roughly 7” x 9”. Place the pie crust onto a large baking sheet covered in parchment paper. Lightly brush the pie crust with the beaten egg white, inward about 1” from the edges.
Spread 1 tablespoon of Dijon mustard on the interior of each pie crust. Scatter the caramelized onions onto the mustard. Layer the zucchini slices over the onions (approximately 3-4 rows). Sprinkle dried thyme onto the zucchini. Top with the tomato slices.
Sprinkle the entire tart with goat cheese, as desired. I used about 3/4 cup of Provençal Herb goat cheese, which included basil among other seasonings. (You can use whatever goat cheese you prefer.) Season with salt and pepper.
Fold the long edges of the pie crust over and then the short edges on each galette. Brush the edges of the crust with egg white.
Bake the galettes for 20 - 25 minutes, or until the crust is golden and the vegetables are softened. Slice and serve warm or at room temperature.