Line 2 large baking sheets with parchment paper and pour a thick, even layer of confectioners sugar over each, about 0.25 to 0.5 inch deep.
Press the whole egg, large end down, into the confectioners sugar to create oval wells across each pan, spacing the indentations about 1 inch apart. Tap the egg to remove excess sugar and repeat until you have at least 24 neat egg shaped molds. Set pans aside.
In the bowl of a stand mixer fitted with the whisk attachment, combine 0.5 cup cold water and the agar agar powder. Stir gently to moisten the agar agar, then let it bloom while you cook the syrup.
In a medium saucepan, combine the granulated sugar, corn syrup, and 0.5 cup water. Stir over medium heat just until the sugar dissolves and the mixture looks clear.
Attach a candy thermometer to the pan, stop stirring, and cook the syrup over medium heat until it reaches 240°F.
Once the syrup reaches 240°F, remove the pan from the heat. Turn the stand mixer on low speed and carefully pour the hot syrup in a thin stream into the bloomed agar agar mixture.
When all the syrup is added, gradually increase the mixer to high speed and whip for about 8 to 10 minutes, or until the mixture is very thick, glossy, and forms ribbons that slowly melt back into the bowl. Add the vanilla bean paste during the last minute of mixing.
Working quickly, transfer the marshmallow mixture to one or two large pastry bags fitted with a large round tip, or with the tip of the bag snipped off to about 0.5 inch opening.
Pipe the marshmallow into the egg shaped wells, filling each indentation level with the surface of the confectioners sugar. Smooth tops lightly if needed. Let the marshmallows sit at room temperature until set and firm to the touch, about 2 to 3 hours.
Once firm, gently lift each marshmallow egg out of the sugar, brushing or dusting off excess confectioners sugar from the surface and sides. Place the cleaned eggs on a clean parchment lined baking sheet.
Place the chopped dark chocolate in a microwave safe bowl and heat for 1 minute on medium power. Stir well, then continue heating in 15 second intervals, stirring between each, until fully melted and smooth.
Using a fork or dipping tool, lower one marshmallow egg at a time into the melted chocolate, turning to coat completely. Lift out, let excess chocolate drip off, then place on a parchment lined baking sheet. Repeat with all marshmallow eggs.
If decorating with sprinkles only, add sprinkles immediately to the wet chocolate before it sets. If using candy melts for extra designs, allow the chocolate coating to firm at room temperature for 1 to 2 hours, or until completely set.
Melt the candy melts according to package directions until smooth. Transfer to a small piping bag or a zip top bag with a tiny corner snipped off, and drizzle or pipe patterns over the set chocolate coated eggs. Add additional sprinkles if desired, then let decorations set completely.
Once all coatings and decorations are fully firm, transfer the marshmallow eggs to an airtight container, layering with parchment if needed, and store at cool room temperature for up to 5 days or in the refrigerator for up to 1 week.