In the bottom of a salad bowl, combine the shallots, mustard and some salt and pepper with the white wine vinegar. In a slow steady stream, whisk in the 1/3 cup EVOO. Add the mixed greens, toss to combine and serve the Fromage Fort toasts alongside.
Preheat oven to 375F.
Arrange the baguette slices on a cookie sheet, drizzle some EVOO over them and transfer to the oven. Toast until golden brown, about 4-5 minutes. Flip them over and toast on the second side until golden, 3-4 minutes. Remove from the oven and cool.
While the bread is toasting, make the Fromage Fort (a.k.a. cheese spread): In a food processor, combine the leftover cheese pieces, garlic clove, white wine and pepper. Process until smooth, transfer to a bowl and mix in the chives and lemon zest. Spread evenly on the cooled toasts.