Heat 1 tsp. oil in a small nonstick or cast-iron skillet over medium heat. Add sausage and cook until evenly browned, about 10 minutes.
Meanwhile, bring broth to a boil in a small saucepan over high heat. Stir in oats and salt; reduce heat to medium and cook, stirring occasionally, until the oats are tender and most of the liquid has been absorbed, about 5 minutes.
Thinly slice the sausage into coins. Stir the sausage, tomatoes, and herbs into the cooked oatmeal. Transfer to a bowl. Top with arugula and pine nuts; drizzle with the remaining 1 tsp. oil. Serve with lemon wedge, if desired.
Tip: To toast pine nuts, cook in a small dry skillet over medium-low heat, stirring constantly, until fragrant, 2 to 4 minutes. Transfer to a small plate and let cool.