Heat the oil in a large nonstick skillet over medium-high heat. Add the ground beef, and cook, stirring frequently, until the beef begins to brown, about 4 minutes. Stir in the chili powder and 1 teaspoon salt, and continue cooking until the meat is cooked through, 2 minutes more. Drain off any excess liquid, and add back 2 tablespoons of it. Reduce the heat to low, stir in the ketchup, sugar, vinegar and 1/2 cup water and simmer, stirring occasionally, until the sauce is slightly thickened, about 8 minutes. Stir in the carrots and corn, and cook, partially covered, until the vegetables are tender and heated through, 5 minutes.
Scoop some sauce onto 1 half of each slider bun, top with a handful of shredded cabbage and a pickle chip and serve.
Never leave a child unattended in the kitchen. Limit the child to tasks that are safe and age-appropriate.
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