In a saucepan, mix together flour, sugar, and salt.

Add eggs to the dry ingredients and whisk until smooth and creamy, ensuring no lumps remain.

Gradually add milk to the mixture, stirring continuously to incorporate it smoothly.

Place the saucepan over low heat and cook slowly, stirring constantly to prevent scorching.

Continue cooking until the custard thickens and becomes smooth.

Remove from heat and stir in vanilla extract.

Serve warm or chilled.