In a large skillet over medium or medium-high heat, add 1 tablespoon oil and sausage. Cook the sausage until it’s browned and mostly cooked through, breaking it up into bite-size chunks along the way, about 3-5 minutes. Transfer to a bowl or plate.
If there is no oil remaining in the skillet, add another tablespoon. Add the brussels sprouts and salt, toss together, then cook over medium heat, undisturbed, for 3 minutes to get some color on the sprouts.
Add the sausage back to the skillet along with the tomatoes and mix everything together. Cover with a lid and cook for 3 minutes over medium-low heat, then remove the lid, give everything a stir, and cook for 2 more minutes. At this point, the tomatoes should have softened and some burst open and the brussels should be cooked through.
Meanwhile, add all the pesto ingredients to a high-speed blender. Use your tamper tool to help encourage blending and blend until smooth, scraping the sides down as needed.
Serve the sausage/sprouts dolloped with the pesto. Squeeze lemon all over (if using). See note for other serving options!