Blender 2.8 How to inset faces and bevel into an oval

I'm looking to recreate the effect seen in the video linked. I've linked it at the start of the part and it runs for about 40 seconds. I'm trying to recreate the rounded inset faces. I can get the faces to inset just fine, but then they do a lot of things in rapid succession and I'm getting lost. Pretty new to blender so if you can be detailed that would be very much appreciated. Imperial Shuttle in Blender 2.8

Solution

Here is what is going in the video from 38:55 till 39:30.

Edge split - splits selected edges from rest of the geometry. This will make hard edges,
Loop cut and slide (Ctrl + R) - makes new edge and let you slide it in place
Select loop of polygons (Alt + select in face select mode)
Separate (P) / Selection - separates selected geometry into new object. This will make editation of this part easier. You can join objects later.
Switch to object mode, select new object, switch to edit mode
Loop cut and slide many times - you can use mousewheel to cut multiple edges at once. Weird shades are caused by two piesces of geometry overlaping each other.
Select all (A)
Inset (I with individual modificator - second I) - insets new polygons in every selected polygon
Invert selection (Ctrl + I)
Remove faces (X, 3)
Select all (A)
Switch to vertex select mode - this is not realy needed. You will see the vertices better though.
Bevel vertices (Shift + Ctr + B) - in the video Bevel edges (Ctrl + B) is actualy used with vertex only modifcator (V) which is the same. During the operation you can use also mouse wheel to make more vertices at once. 14a. Extrude menu (Alt + E) then Extrude faces along normals - you can use inset while holding Ctrl here. It's doing basicaly the same thing. 14b. Well then he undid it and used solidify modifier instead. The advantage over extrude or inset is thaht you can change the depth of panels later easily.
Switch back to old object
And finaly Extrude along normals in faces mode (Alt E, 2)

Happy blending