Heat a skillet over medium heat and add the butter. Place your thick bread slices in the pan and toast them until they are a deep, uniform golden brown. Once finished, let the bread cool on a wire rack for a moment to prevent steam from softening the bottom.
In a small bowl, stir the softened cream cheese and Greek yogurt until the texture is velvety and smooth. Fold in the fresh dill, minced chives, and garlic powder.
Use a sharp serrated knife to cut your tomatoes into thick, even slabs. Thick-cut tomatoes are essential for a top-notch sandwich because they provide a “meaty” texture that balances the hearty sourdough bread. Pat the slices gently with a paper towel to remove any loose surface water.
Lay the tomato slices out and sprinkle them with flaky sea salt and cracked black pepper. Let the salt sit for three minutes.
Apply a very thick layer of the herb spread to one side of each toasted slice. Be generous and spread it from edge to edge to create a protective barrier.
Place two or three seasoned tomato slabs onto the prepared bread slices, overlapping them slightly to cover the entire surface. This ensures a consistent fruit-to-bread ratio in every mouthful.
Place the remaining bread on top, herb-side down, and press very gently with your palm to bond the layers together. Use your serrated knife to cut the sandwiches in half on a diagonal.