Place squash cut side up on a paper towel-lined baking sheet. Generously sprinkle with kosher salt. Let sit 15 minutes to extract some moisture from the squash.
Heat a heavy skillet over medium heat; add olive oil and ground chorizo. Cook until chorizo is very well browned, 6 to 8 minutes, breaking up the meat into fine pieces with a wooden spoon as it cooks. Remove from heat. Leave about 2 tablespoons of rendered fat in the pan; remove the rest. Stir olive oil, vinegar, and freshly sliced mint into the chorizo mixture.
Preheat an outdoor grill for medium-high heat and lightly oil the grate. Blot off moisture from squash with a paper towel.
Grill squash rounds, turning them often, until tender and nicely charred, about 3 minutes total per side. Transfer to serving dish. Top with warm chorizo vinaigrette. Garnish with more chopped mint.
