Farmers Market Hash with Poached Eggs

grape seed or canola oil, seperated

(3/4 lb) red new potatoes

(1/4 lb) green beans, sliced into 1″ lengths (roughly 3/4 cup)

(6-7 whole) mini sweet peppers, stems removed

ear of corn, stripped of kernels

grape or cherry tomatoes, sliced in half

medium garlic cloves, finely minced

whole eggs

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good-quality parmesan cheese (optional)