Place eggs in a single layer in a saucepan and cover with cold water by 1 inch. Bring to a rolling boil.

Remove from heat immediately, cover with a lid, and let stand for 12 minutes. Transfer eggs to an ice water bath for 10 minutes to stop the cooking process.

Prepare natural dyes by simmering each pigment source (cabbage, turmeric, or beets) in 2 cups of water for 20 minutes in separate pots. Strain liquids into glass jars and discard solids.

Incorporate 1 tablespoon of white vinegar into each dye jar to act as a mordant for the calcium carbonate shells.

For botanical patterns, press a leaf or flower firmly against the dry egg shell. Wrap the egg tightly in a nylon square and secure with a rubber band to create a vacuum seal.

Submerge the prepared eggs into the dye baths. Transfer jars to refrigeration and steep for 4 to 12 hours depending on desired color saturation.

Remove eggs from dye, carefully snip the nylon, and remove botanical elements. Allow eggs to air dry on a wire rack.

Apply a minimal amount of vegetable oil to a soft cloth and buff each egg to enhance the depth of color and provide a subtle luster.