Preheat oven to 375 Fahrenheit. Brush sliced baguette with 2 tablespoons of the olive oil. Season. Bake until slightly golden, turning halfway through, about 12 minutes. Also toast the walnuts for 6 minutes. Remove and let cool.
Place the arugula, remaining 2 tablespoons of oil, cider vinegar and honey in a bowl. Season well with salt and pepper. Mix together.
Cut the garlic clove in half and rub the toasted baguette with the cut sides.
Assemble the crostini by starting with arugula, then burrata, then top with 2 walnut halves or pieces. Season again if necessary.