Preheat the oven to 350 degrees F. Spread the fava beans and shallot out onto a baking sheet. Transfer the baking sheet to the oven and bake for 20-25 minutes. You'll know the fava beans are done when their shells appear weathered and a little wrinkly. Allow the fava beans to cool slightly, about 5 minutes, before handling.
To a large skillet, melt 1 tablespoon of butter with a two teaspoons of olive oil. Add the bread, along with a pinch of salt and pepper. Cook until the bread is lightly golden brown on all sides. Transfer the bread to a bowl and set aside.
To shell the fava beans, snip off their tops with a knife; squeeze from the bottom of the pod, pushing out all of the beans. The small ones don't need to be shucked twice, but the bigger ones do. Take your nail, and gently rip off the tops, peeling away the outer shell. Inside will be a bright green bean. Repeat until you've gone through all of the beans. Next, remove the outer shell of the shallot and mince.
To the same skillet you cooked the bread in, add the minced shallot, the remaining 1 tablespoon unsalted butter, 1 tablespoon olive oil, red wine vinegar and fava beans. Cook over medium-low, mixing the entire time, adding a pinch of two of salt and pepper, for about 2-3 minutes. Add the dill and bread, tossing everything together. Transfer the salad to a plate. Top with the segments of blood orange and the burrata. Serve warm.