Whip room temperature egg whites in a mixing bowl using an electric hand mixer with a whisk attachment on medium-low speed until the eggs are very foamy.
Heat ½ cup (99 grams) granulated sugar and water in a small saucepan over medium high heat until the sugar reaches 244°F (118°C) on a digital thermometer. Don't stir the mixture as it's cooking as this could cause it to crystallize.
Once the sugar has reached temperature, turn the mixer speed to medium-high and slowly pour the sugar syrup down the side of the mixing bowl. Be sure the sugar runs down the bowl and doesn’t hit the whisk attachment or it will splatter. Continue to whip up on medium-high speed until stiff peaks form. To test the meringue stiffness, pull the whisk out. A stiff peak should stand straight up.
Beat egg yolks and remaining ¼ cup (49 grams) of granulated sugar in a separate mixing bowl using a hand whisk until the eggs are pale in color. Add room temperature mascarpone, Baileys Irish cream, and sea salt and mix until incorporated and creamy in texture.
Carefully fold the meringue into the egg yolk mixture using a silicone spatula.
Place the cooled espresso in a shallow dish. Break two lady fingers in half, then dip in espresso for 1 - 2 seconds, just until they have slightly absorbed the liquid. Place the lady fingers in a martini serving glass. Repeat for the remaining four martini serving glasses.
Evenly layer the meringue and egg yolk mixture on top of the ladyfingers, then use an offset spatula to smooth out the top.
Dust a light layer of cocoa powder on top of each martini glass using a fine mesh strainer.
Cover each martini glass with plastic wrap and chill in the refrigerator for at least 2 hours before serving.