In a large, heavy pot, such as a Dutch oven, over medium-high heat, heat the oil until shimmering. Use your hands to break the sausage into small pieces directly into the pot. Add the onion and season everything with a big pinch of salt. Cook, stirring occasionally, until the sausage is browned, about 10 minutes, adjusting the heat as needed to prevent scorching.
Add the garlic and the tomato paste and cook, stirring, until very fragrant and most of the moisture from the tomato paste has evaporated, about 1 minute. Stir in the broth. Increase the heat to high and bring the mixture to a boil. While it’s coming to a boil, scrape the bottom of the pot with a wooden spoon to dislodge any stuck-on pieces. (Flavor!) Once the mixture comes to a boil, reduce the heat to low, season to taste with salt, and stir in the farro and kale.
Partially cover the pot so the steam can escape, and simmer, stirring occasionally, until the kale and farro are tender, 30 to 35 minutes. Stir in half of the lemon zest and juice, and season to taste with more lemon and/or salt, if desired. Serve hot.