Preheat the oven to 375 degrees.
Heat a saute pan on medium heat. Once hot, add the butter and half of the oil, then saute the celery, carrot, and shallot until they begin to color. Once soft and caramelized set aside in a bowl. Add the remaining oil to the pan and saute the spinach until wilted, season with salt, then set aside in a bowl.
Season the steak well on both sides with salt and pepper.
Roll out the pastry to 1/8 inch thickness using a rolling pin. Cut into 5 inch circles using a bowl, food ring, or wide mug. (2 per portion)
To assemble: Lay a puff pastry round on a parchment lined baking sheet and brush with egg whites. (Repeat for all portions). Place the steak on the puff pastry round, top with spinach and the shallot mixture.
Lay the remaining circles of pastry on top, then smooth it down on top of the filling, being careful not to tear the pastry. Press the edges of the top circle onto the edges of the base to seal each one.
Brush the galettes all over with egg yolk and refrigerate for 10 minutes
(Optional) Take a knife and starting at the top in the center, score half circles down the sides, being careful not to pierce all the way through the pastry
Bake in the oven for about 20 minutes until golden brown. Set aside to rest for 5 minutes.
Meanwhile, place the broth, wine, thyme, and tomato paste into a saucepan on medium heat. Bring to a simmer to concentrate flavor and reduce to a smooth thickened consistency. (Should coat the back of a spoon).
Serve the galette with sauce. Garnish with thyme.