Preheat the oven to 350 degrees. Grease and flour a standard bundt pan.
In a large bowl, mix together beaten eggs and sugar. Add vanilla and salt.
Slowly add half of the melted butter to mixture. Mix until well combined. Stir in one cup of flour. Mix until well combined. Mix in remaining butter to mixture. Stir in another cup of flour. Stir until batter is even with no lumps.
Bake in oven for 40 - 50 minutes, or until inserted toothpick comes out clean.
Let cake cool on wire rack upright in pan for 15 minutes. After initial cooling, gently turn pan over and tap until cake slides out.