Bring a large pot of salted water to a boil. Cook the pasta according to the package directions. Reserve at least 1 cup of pasta water.
While the pasta cooks, add the olive oil to a large pan over medium heat. When its warm add the thinly sliced onion. Cook for 2-3 minutes until mostly cooked. While the onion is cooking chop the carrots into bite sized pieces. Add garlic and cook an additional minute.
Add the carrots and 2 cups of the vegetable broth to the pan. Cover and turn the heat to medium low. Let it simmer for 3-4 minutes, until the carrots are fork tender.
Carefully transfer the mixture to a blender (or use an immersion blender). Add the remaining vegetable broth, the heavy cream, dijon mustard, brown sugar, salt, and pepper. Blend until smooth.
Pour the sauce over the cooked, drained pasta. Stir to combine, adding a bit of reserved pasta water as you do (the amount of pasta water added is up to you - add until the sauce is your desired consistency).
For the toasted breadcrumbs, blend the slice of bread in a food processor. Pour the breadcrumbs into a small pan with the olive oil and garlic salt over medium heat. Stir until the breadcrumbs are golden brown, about 3-4 minutes.
To serve, scoop the hot pasta into bowls and top with toasted breadcrumbs and fresh basil. Enjoy!