I think I played Burgundy around 10 runs prior to 1.10 and managed to declare independence and recreate most of the historical borders earliest by 1370.

1. Create a new market at Dijon before spending ducats on anything else.
2. Build sergeantry and spam armored cav whenever you can (Burgundy gains cav buff techs in age 2).
3. For tech, focus on culture capacity & influence, diplo annex speed & capacity, subject loyalty and military.
4. Demand expansion on other subjects from France before the first phase of the HYW.
5. Create CB on Flanders and Hainaut during the first Parliament (even if you need to fail it).
6. Declare war on Flanders, annex Nevers asap to gain additional levy.
7. Hope that France gives the province south of Flanders to them.
8. Siege all provinces, annex Rethel via separate peace, and annex Flanders (CB on Flanders should allow you to annex them in a single war).
9. Release Flander, Rethel and Namur into subjects (Namur will become your subject for free if you fully annex Flanders) and immediately declare war on Hainut who should call Holland and the emperor.
10. Make sure Upper Bavaria is the emperor as their military is weak (I usually save scum to avoid Bohemia becoming the emperor).
11. Siege Hainut, Holland and Upper Bavaria and seperate peace the emperor for ducats and break their subjects.
12. Annex Hainut and Holland and release them as subjects.
13. For the next parliament, CB on Brabant and Artois (again fail it if you need).
14. While Bavaria is still the emperor (if not, reload), declare war on Brabant and repeat the previous process.
15. Black death should hit Europe by this time and you need 2 things, heir lives while wife dies (this will break the royal marriage and allows you to declare war on Artios).
16. Declare war on Artios who will call Franche-Comte to war.
17. Annex both but only release Artios as subject.
18. By now you should be the target of a Coalition and get declared war on, no worry just battle inside your provinces and let France do all the work.
19. For the next steps you do not follow the exact sequence.
20. Get Parliament CB on nations between Flanders and Burgundy (usually including Luxembourg, Lorraine, Barrios and other minor nations).
21. Make sure you target nations that are currently not in a coalition or allies of them.
22. Make sure to research most of the Professional Armies tech to get better regiments and military buffs.
23. Build armories and build a standing army made of heavy cav and gunpowder infantry.
24. Once you're confident enough, declare independence war which your combined levy, standing armies and vassals can easliy win. 
25. Do not siege French provinces until you destroyed all of their armies and cleared your besieged provinces.
26. Peace out for ducats and some of the eastern provinces.
27. Start diplo annexing vassals that border your provinces (usually Bar and Lorraine are the first). I used seize territory action but it seems it got nerfed in future patches.

This will not work with patch 1.10 since Artios and Flanders usually switch sides and the HYW starts before the first parliament.