Step 1

Cook shallots and oil in a medium saucepan over medium heat, stirring occasionally, until shallots are golden brown, about 4 minutes. Using a slotted spoon, transfer shallots to a paper towel–lined plate; season with salt. Let shallot oil cool.

Step 2

Whisk both vinegars, honey, and ¼ cup shallot oil (reserve remaining oil for another use) in a large bowl; season with salt and pepper. Add radicchio and arugula and toss to coat. Serve salad topped with crispy shallots and Parmesan.