Preheat the oven to 400°F (200°C).
Slice the baguette on the diagonal into 1/4-inch thick slices using a serrated knife.
Arrange the slices in a single layer on a baking sheet.
Whisk together the melted butter and olive oil; if your butter is unsalted, add a small pinch of salt.
Brush the tops of the baguette slices with the butter–oil mixture.
Bake the slices for 8–10 minutes until the bottoms are golden and crisp; check and flip if needed so they toast evenly. Remove and let cool.
Meanwhile, combine 1/4 cup Greek yogurt, the cream cheese, chopped dill, and lemon juice in a food processor. Process, scraping the sides, until mostly smooth.
Add additional Greek yogurt a little at a time (up to about 3/4 cup total) until the mixture is soft and spreadable but not runny; season with salt to taste and process again to combine.
Cut the smoked salmon into pieces that will fit on each crostini.
Spread about 1 teaspoon of the yogurt–cream cheese mixture on each cooled toast, top with a piece of smoked salmon, and add a small additional dollop of the spread on top if desired.
Garnish each crostini with a few capers or a small sprig of fresh dill and serve.