Preheat oven to 350 degrees. Grease a 8" springform pan or grease a regular 8" cake tin and line with parchment paper.
Gently melt the chocolate and butter in a small saucepan over medium-low heat. Turn off the heat once chocolate has melted. Stir until butter and chocolate are both melted and incorporated. Add lime zest and salt. Set aside to cool as you move on to the next step.
Using a mixer with the whisk attachment, whisk the egg yolks with 3 1/2 tbsp of sugar until thick and creamy. Pour into another bowl.
Clean and thoroughly dry bowl and whisk attachment. Beat the egg whites until completely foamy. Continue to whisk, adding the remaining (7 tbsp) of sugar one tablespoon at a time. Whisk well after each addition and continue until slowly lifting the whisk out of the mixture leaves a soft peak.
Fold the egg yolk mixture into the chocolate with a plastic spatula, then fold one third of this chocolate mixture into the egg whites. Once basically combined but still marbled, fold in the next third of the chocolate mixture. Then the final third.
Sift in half of the flour and gently fold in until nearly combined. Sift in remaining flour and gently mix again. Try to keep as much air in the batter as possible.
Spoon the batter into the prepared pan and bake for 30 minutes until a toothpick comes out mostly clean, with just a couple crumbs. If using a springform pan, release side piece and let cool. If using a regular cake pan, cool in the pan and pull out using the parchment paper.