Cook rice according to package instructions. Set aside.
Meanwhile, in a large skillet, heat olive oil over medium high heat. Add onions and cook until translucent. Stir in garlic and celery and season with salt and pepper. Cook until vegetables are soft, about 5 minutes.
Add in mushrooms and tarragon and cook until mushrooms release their juices and the liquid evaporates, about 5 more minutes. Add in spinach and cook until wilted. Stir in sun dried tomatoes, then remove from heat and let cool slightly.
In a large bowl, whisk together eggs, mustard, and broth. Add in vegetable mixture and rice and stir to combine.
Generously grease a loaf pan with olive oil. Pour in vegetable mixture and smooth to flat with a spatula. Bake for 40-45 minutes, until edges are nicely browned. Let cool slightly, then run a knife along edges and flip onto platter.