Preheat oven to 375 degrees. On a large rimmed baking sheet, toss nuts with 1 teaspoon oil and cinnamon; season with salt and pepper. Bake until golden, 4 to 6 minutes; set aside to cool.
Spread baguette slices on same baking sheet and brush with remaining 3 teaspoons oil; season with salt and pepper. Bake until lightly toasted, 10 to 15 minutes, rotating pan halfway through; set aside to cool.
Meanwhile, in a medium bowl, stir together cheese and 2 tablespoons water until smooth; stir in cranberries and thyme. Season with salt and pepper. Divide goat cheese among bread slices and top each with a walnut and thyme leaves.
To make ahead, refrigerate goat cheese mixture, covered, up to 1 day. Store roasted walnuts at room temperature, up to 1 day.