For the browned butter

Timings are quite crucial here and it might seen stressful the first time you make it but you will get used to it quickly. Butter sauces come together quite quickly, so you will be making them and boiling your pasta simultaneously. If you know the browned butter takes around 4 minutes then take that into consideration when you start the pasta.

1. Melt the butter in a large frying pan over medium heat.
2. Add in the sage leaves as the butter is melting and bring to a sizzle. 
3. Add a big pinch of salt then continue to cook, swirling the pan from time to time until it begins to foam and the milk solids separate and brown.
4. Add your pasta straight in, trying not to get any pasta water in.
5. Serve and enjoy!

For the emulsified butter sauce

As I mention above, you will get used to the timings.

1. Melt the butter in a large frying pan over medium heat until it begins to sizzle.
2. Lower the heat and add the lemon juice, whisking vigorously while shaking the pan at the same time.
3. Add 1/4 cup pasta water and repeat, making sure you whisk fast to bring the liquids together.
4. Add your pasta straight in and let it gently bubble away for a minute before serving.
5. Add more pasta water if you need.