In a large 10" to 11" skillet over medium-low heat, heat oil. Add garlic and red pepper flakes and cook, stirring, until garlic begins to soften and oil turns a little golden from the flakes, 2 to 3 minutes. Add tomato paste and cook, stirring, until garlic is lightly golden and tomato paste breaks up into tiny clusters, about 1 minute.
In a medium bowl, combine tomato passata and broth. Increase heat to medium-high. Lay spaghetti flat in skillet. Add 1 c. tomato broth and cook, undisturbed, until liquid evaporates, leaving a thickened paste on bottom and around spaghetti, 4 to 5 minutes.
Using a metal spatula, unstick spaghetti from skillet as it begins to burn or char on one side. Add salt and 1 cup tomato broth and continue to cook, stirring frequently, until liquid is nearly evaporated and turns into a thickened sauce, 4 to 5 minutes. Gradually continue to add tomato broth and cook, stirring occasionally, until spaghetti is al dente, charred, and sauce adheres to the pasta, 25 to 30 minutes.
