Whisk the mayonnaise, garlic, and lemon juice in a small bowl until well combined. Set this aside to allow the garlic flavor to permeate the sauce while you prepare the main dish.

Heat the oil in a 12-inch skillet over medium-high heat until the oil shimmers. Add the noodles and cook, stirring frequently, until they are deeply golden and smell toasted, about 3 to 5 minutes.

Reduce the heat to medium and stir in the onion. Cook until the onion is softened and translucent, about 4 to 6 minutes.

Stir in the garlic, smoked paprika, and red pepper flakes. Cook until the spices are fragrant, about 30 seconds, taking care to keep the mixture moving so the garlic does not burn.

Stir in the tomatoes, broth, and chickpeas. Bring the mixture to a simmer, then cover and cook until the noodles are tender and the liquid has been absorbed, 8 to 10 minutes.

Remove the skillet from the heat and stir in the parsley. Serve warm with a generous dollop of the prepared aïoli on top of each bowl.