Brown sausage: Preheat oven to 425°F with a rack in the center. Bring a medium pot of salted water to a boil. Peel and finely chop 2 large garlic cloves. Halve sausages lengthwise to remove from casing. Heat 1 tablespoon oil in a medium saucepan over medium-high. Add sausage, cook, breaking into smaller pieces with a wooden spoon, until browned and crispy on edges, 5–8 minutes.
Build sauce: Add 1⁄2 of the garlic to sausage and cook, stirring until fragrant, about 1 minute. Add 1⁄3 cup of the tomato paste and cook, stirring, until it darkens slightly, 1–2 minutes. Stir in 2 cups water, broth concentrate, and 1 teaspoon sugar. Bring to a boil, then simmer over medium heat until flavorful and reduced to 2 cups, 16–18 minutes. Keep warm.
Make garlic bread: Meanwhile, finely grate Parmesan. Split roll horizontally. Brush cut sides generously with oil and sprinkle with remaining garlic and 1⁄3 of the Parmesan. Season with salt and pepper and bake on a sheet of foil, directly on the center oven rack until golden and crisp, 5–7 minutes. Drizzle with oil and cut each into 4ths.
Prep lettuce & dressing: Remove any wilted outer leaves from lettuce. Half lengthwise, then cut crosswise into 1-inch pieces, discarding the end. Into a large bowl, grate 1⁄4 teaspoon lemon zest and squeeze 1 tablespoon lemon juice. Add 2 tablespoons oil and a pinch each salt and pepper and whisk to combine.
Cook pasta: Stack fresh pasta sheets and cut crosswise into 1⁄2-inch wide strips. Add to boiling water and cook, stirring to prevent clumping, until al dente, about 2 minutes. Drain well and return pasta to the pot. Add half of the bolognese and toss to combine.
Finish & serve: Add lettuce and half of the remaining Parmesan to dressing and toss to combine. Serve pasta, topped with remaining sauce and Parmesan, with salad and garlic bread alongside. Enjoy!