How do you create a rounded, inset beveled edge? TL;DR How do you create a smooth, inset, rounded, beveled edge?

Hello! I'm sorry for the mundane question, but I'm a bit stuck. I'm trying to learn Blender and as an exercise I'm modeling a cabinet from my living room.

This cabinet has a beveled, rounded, inset edge:



So far, I've managed to create this in Blender: (bevel modifier with 3 segments)

Now here comes the problem. I'm trying to apply a subdivision modifier to smooth the bevel, but of course this smooths the entire mesh. I've thought of using 2 seperate objects but I felt like I was just avoiding the problem and it didn't even solve it completely.
So my question is this: How do you create a smooth, inset, rounded, beveled edge?
Similiar to creating the control edge loops manually (as stated in stauVictors answer), you can create them procedurally with the bevel modifier. Using a bevel modifier before a Subdivision Surface modifier, is common practice to prevent smoothing on sharp edges.

Create a vertex group for the edges, which are supposed to stay sharp and assign the edges to it

Then add a bevel modifier and select that group as the Vertex Group of the modifier. If you use more segments in the Bevel modifier, the following subdivision modifier will have less effect on the beveled segments.



Edit from Coffeehouse's comment: As an alternative to the Vertex Group, you can choose weight as the Limit Method and create Bevel Weights for the mesh.