1. Preheat your oven to 375° F. In a 7.5 quart dutch oven, melt the butter over medium-low heat. Add the diced onion, carrots, and celery, and sauté for about 7-10 minutes, until they begin to soften. Add the minced garlic and cook for another 1-2 minutes until fragrant.
2. Sprinkle the flour over the vegetable mixture and stir well to coat. Cook for 2-3 minutes, stirring constantly.
3. Slowly pour in the chicken broth, stirring constantly to prevent lumps from forming. Add heavy cream, tarragon, thyme, salt, and pepper. Stir until the mixture thickens and comes to a gentle simmer. Add the chicken, stirring to combine. Remove the pot from the heat.
4. Roll out the croissant dough sheets, score edges and press them together to create one large sheet of dough. Set the lid on top of the dough and press gently. Remove the lid and cut out the shape of the lid, transfer the dough circle and cut 4 vents. Using a rolling pin, transfer dough to the top of the vegetable mixture and brush with egg wash.
5. Cut small triangles into the remaining dough, about an inch and a half long. The triangles should have two long sides and one short, like a traffic cone or witch's hat. Pull the bottom of the triangle out just a bit and roll the dough away from yourself gently. Turn the ends of the dough in and press gently to form a miniature croissant. Repeat with remaining dough. 
6. Arrange the mini croissants atop the dish and brush with egg wash. Place the dutch oven in the preheated oven and bake for 15-20 minutes, or until the croissant dough is puffed and golden brown. Once baked, remove the dutch oven from the oven and let it cool for a few minutes before serving.

Pro Tip: Have remaining dough? Invert the lid and bake extra mini croissants directly on the lid. You can never have too many mini croissants.