Heat the agave in a small saucepan over medium-low heat until it thins out and is warmed, about 5 minutes. Add the vinegar and shallot and gently simmer, swirling the pan a few times, until the sauce has reduced and thickened to the consistency of maple syrup and coats the back of a spoon, about 50 minutes.
Remove the shallot and add a good pinch each of salt and pepper. The reduction can be stored covered at room temperature for up to 3 months.
To Prepare Scoty's Marinara Sauce:
Working in batches, put the tomatoes, along with their juice, in a food processor or blender and puree just until semi-smooth; you want a little bit of chunky texture.
Put a medium pot over medium heat and add the oil. When the oil is hot, add the onion, garlic, and carrot, season with salt, black pepper, and the red pepper flakes, and sauté until the vegetables are soft, about 10 minutes.
Add the pureed tomatoes, stirring to combine, and bring to a boil. Reduce the heat to medium-low and simmer, uncovered, until the sauce thickens, about 45 minutes. Season the sauce with more salt and black pepper, to taste. Remove from the heat, stir in the baking soda, making sure it dissolves, and add the basil and butter substitute.
Once cooled, the sauce can be refrigerated covered for up to 3 days or frozen for up to 2 months.
To Prepare the Dish:
To prepare the balsamic mushrooms and shallots for the sauce: Preheat the oven to 400°F.
Put the mushrooms and sliced shallots in a mixing bowl and drizzle with the oil. Pour in the balsamic reduction, season with salt, black pepper, and ¼ teaspoon of the red pepper flakes, and turn the mushrooms and shallots over so they are well coated. Spread the vegetables out in a single layer on a baking sheet that has been coated with nonstick cooking spray and roast for 20 to 25 minutes, until tender and deep brown. Set aside. (The roasted mushrooms and shallots can be prepared a couple of hours in advance, covered, and held at room temperature.)
Bring a large pot of salted water to a boil.
Meanwhile, prepare the sauce: Put a large sauté pan over medium heat and add 3 tablespoons of the butter substitute. When it has melted, toss in the minced shallot and garlic and cook, stirring, until softened, about 1 minute. Season with salt, black pepper, and the remaining ¼ teaspoon red pepper flakes, add the roasted balsamic mushrooms and shallots, and toss until well coated. Pour in the sherry and cook for 30 seconds to evaporate some of the alcohol. Stir in the marinara sauce and simmer until heated through, about 5 minutes.
When the water comes to a boil, add the pasta, give it a couple of good stirs with a wooden spoon, and cook until tender yet firm. Drain the pasta well, reserving ¼ cup of the starchy cooking water to use in the sauce if necessary.
Add the linguine to the sauce, tossing with tongs to coat. Add the remaining 1 tablespoon butter substitute and the basil, season with salt and black pepper, and toss to distribute evenly. If the sauce gets too thick, thin it with enough of the reserved pasta water so the linguine is thoroughly coated.
Divide the linguine among plates or transfer to a bowl. Serve immediately.
Notes
You can substitute maple syrup for agave nectar. Make-Ahead tip - make the sauce or mushroom mixture the day before to save time.