Toast the stars
Warm the oil in a soup pot over medium heat. Add the star pasta and stir constantly until most pieces are golden-brown and smell toasty and nutty. Be careful, they go from perfect to burnt quickly. Scoop the toasted stars out and set aside, leaving the oil in the pot.
Build the base
If using fresh shallot/onion, add it to the same oil and sweat until translucent and sweet-smelling. Add the fresh minced garlic and cook until fragrant, about 30 seconds. If using powders, skip this step and add them later with the cumin.
If using fresh chile, add it now and cook briefly.
Add the canned tomatoes (or tomato paste) and cook down for 3-5 minutes, stirring, until the tomato darkens slightly and loses its raw edge.
Bloom the spices
Stir in the ground cumin, Mexican oregano (if using), cinnamon (if using), and any garlic/onion powders. Let them sizzle in the tomato for 30 seconds until fragrant. If using smoked paprika or chipotle, add it here too.
Simmer
Pour in the broth and add the bay leaf. If using carrot or other firm vegetables, add them now so they soften. Bring to a gentle boil, then reduce to a simmer.
Once the carrots are nearly tender, return the toasted stars to the pot. Simmer gently until the stars are slightly soft. Stir occasionally so they don't stick.
Finish
Remove the bay leaf. Taste and adjust salt and pepper. The soup should taste savoury and bright.
Turn off the heat and stir in the lime juice or vinegar. This last hit of acid makes the tomato pop so don't skip it.
Serve hot. A drizzle of good oil on top is nice if you have it. This soup keeps okay, but the stars will swell and soften over time; it's best eaten the same day.