Combine rice vinegar, water, sugar, salt, and smashed garlic in a small saucepan over medium heat.
Stir until sugar and salt dissolve, about 2 minutes.
Place sliced jalapeños in a heatproof jar and pour warm brine over them.
Let sit for at least 15 minutes while you prep other ingredients.
Heat a 10-inch cast iron skillet over medium heat.
Add the chorizo, breaking it up with a wooden spoon as it cooks.
Render for 5-6 minutes until the fat is released and the meat is crispy at the edges.
Add the minced garlic and cook for 30 seconds until fragrant.
Push the chorizo to one side of the skillet.
Reduce heat to medium-low.
Add the shredded Oaxacan cheese, spreading evenly around the chorizo.
Let the cheese melt undisturbed for 1-2 minutes until edges bubble.
Gently fold the chorizo through the melting cheese.
Add the quick pickled jalapeños and a splash of brine, folding once to distribute.
Remove from heat while cheese is still molten.
Top with additional pickled jalapeños and fresh cilantro.
Squeeze lime over the top.
Serve immediately with Firehook Sea Salt crackers.