Zucchini Fennel Noodles

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1 tablespoon plus 1/4 cup extra-virgin olive oil

8 slices prosciutto, sliced into 1/2-inch ribbons 

3 large zucchini, ends trimmed, sliced lengthwise 

1 large bulb fennel, very finely sliced, plus 2 tablespoons chopped fronds

Kosher salt and freshly ground black pepper 

1 teaspoon Dijon mustard 

1 clove garlic, crushed 

Zest and juice of 1 lemon

1/2 cup shaved pecorino 

2 tablespoons chopped fresh chives, for garnish