Prepare and sterilize the canning jars and lids. Bring a half-filled water-bath canner to a simmer and keep additional hot water ready.

Heat the oven to 250°F and keep clean jars in the oven for 15–20 minutes. Keep the lids in barely simmering water and assemble the remaining canning equipment.

Wash the blackberries, place them in a large pot, and mash to a pulp. Stir in the sugar, 1/2 cup mead, honey, and lemon juice. Tie the thyme into a bundle, wrapping it in cheesecloth if desired.

Bring the mixture to a boil over medium-high heat, stirring constantly. Add the optional butter and thyme bundle. Maintain the boil and skim excess foam as needed.

Boil, stirring constantly, until the jam thickens and reaches 220°F, about 15–20 minutes. Remove the thyme and stir in the remaining 2 tablespoons mead.

Ladle the hot jam into hot jars, leaving 1/2 inch headspace. Wipe the rims, apply lids, and screw on the rings.

Process the sealed jars in a boiling-water bath for 10 minutes, ensuring the jars are covered by 1–2 inches of water.

Remove the jars and allow them to seal. Refrigerate any unsealed jars and use them within a few weeks; properly sealed jars can be labeled and stored in the pantry.