Melt butter in a large saucepan over medium heat. Add chopped shallot or onion, cardamom pods, 3/4 tsp. salt, 1/2 tsp. pepper, coriander, and cinnamon. Stir and let cook for 2-3 minutes until shallot or onion softens slightly. Then add farro (be sure to rinse it thoroughly beforehand) and bay leaf and stir to coat with butter and seasonings. Let farro toast 2-3 minutes over medium heat before adding the vegetable broth. Bring broth to a vigorous boil, then reduce heat to medium-low to keep it at a gentle boil until farro cooks through (approximately 18-20 minutes for semi-pearled, see TIP A for more detail). Cooked farro should be tender and chewy, like al dente pasta (not mushy). It will not absorb all of the broth, so be sure to check it periodically much like you would when cooking pasta.
TIP A: Pearled and semi-pearled farro are the most common varieties found in grocery stores today because they keep longer and cook faster. "Pearling" simply means that the grains were polished to remove or partially remove the outer bran layer that tends to turn rancid a lot earlier than the rest of grain. Here's the troubling part...the bran layer is very nutrient-rich. In fact, pearled or semi-pearled farro is not technically a whole grain because this outer bran layer has been removed. But, don't fret! With farro (and barley too) nutrients are actually distributed more evenly throughout the grain—more so than other grain types. So when the farro bran is polished or partially polished away, a lot of healthy nutrients still remain. Bottom line, pearled and semi-pearled farro are still nutrient-rich and much better for you than many other processed grain choices. I often opt for semi-pearled farro (or "scratched" as it is sometimes described) which has some of the bran remaining and cooks in about 20-25 minutes. If you go with whole grain farro, just be sure to adjust your cooking time (usually double).
TIP B: You might have heard that the difference between a broth and stock is that a stock is prepared with the bones, whereas a broth is not. This is sometimes true, but not always the case...and certainly not the case when it comes to vegetable stock! So, what's the difference? Technically, I believe the difference is in how the products are used. A stock is used to make something else like a sauce, gravy, or puréed soup, while a broth can be consumed as a finished product. In appearance, I find that stocks are richer in color and thicker in consistency. When it comes to vegetable-only based varieties, often vegetable stock will have a high mushroom content to give it a deeper color. This is great if you want a mushroom-forward flavor. It's not so great if you don't! I almost always use vegetable broth (and check the label to ensure that it does not contain mushrooms) because I want a more neutral, seasoned flavor. Mushrooms—particularly if they are listed as one of the first few ingredients in the ingredient line—can be really over-powering and change the intended flavor of your dish.