Make sure the butter is chilled before using in the recipe. Dice the butter into smaller pieces, then place into the freezer while measuring the dry ingredients. In a large mixing bowl, combine all the dry ingredients: flour, sugar, salt, baking powder and soda, and seasonings. Add the butter next and using a pastry butter or two large forks, cut the butter into the flour until the mixture resembles fine crumbs. You can also use a food processor for this step but be careful not to over-heat the butter; pulse slowly.
Next, prepare the wet ingredients. Combine the sour cream, milk and eggs in a large measuring cup and whisk together until the eggs are well beaten. Make a well in the center of the butter and flour mixture and add the liquids. Use a spatula to fold all the ingredients together until a sticky dough forms (dough needs to be sticky, don't add more flour!). Add the cheddar cheese ham and chives, then mix again until the ingredients are uniform throughout.
Line the work surface with a sheet of plastic wrap and transfer the dough onto the plastic and wrap tightly. Shape the dough into a flat disk, about 1 inch tall. Place the dough into the refrigerator to chill for at least 15 to 20 minutes, or leave until ready to bake.
Preheat oven to 350F. Line a large baking sheet with a silicone mat or parchment paper. Remove the plastic wrap from the scone dough and using a sharp knife, section the disk into 8 equal pieces. Carefully transfer the scones onto the prepared baking pan, spacing the scones about 1 1/2 to 2 inches apart. Top each scone off with more cheddar cheese and chives.
Bake in preheated oven for 28 to 30 minutes, until golden brown. Remove from oven and cool on a wire rack for 10 to 15 minutes before serving. If you have extras, let the scones cool down completely, then place the leftovers into an airtight container or large ziplock bag and into the refrigerator. Warm up in the microwave when ready to enjoy!