Mini-ITX + dual Intel LAN motherboard

You are likey limited to server or workstation class, or the odd industrial with embedded cpu.  asrock rack makes a bunch, they are the server arm of asrock.  Asus has a few as does msi I believe.  .  A good number have embedded amd or intel processors.  Here's an example with embedded low end epyc 3101 and dual 10gb.

www.asrockrack.com/.../productdetail.asp

Here's one you can drop a Ryzen3 3000 cpu on which also has dual 10Gb intel nics.  https://www.asrockrack.com/general/productdetail.asp?Model=X570D4I-2T#Specifications

Here's an asus example with dual intel gig. https://www.asus.com/ca-en/Commercial-Servers-Workstations/P10S-I/

None of these are what I would call inexpensive.

You are likey limited to server or workstation class, or the odd industrial with embedded cpu.  asrock rack makes a bunch, they are the server arm of asrock.  Asus has a few as does msi I believe.  .  A good number have embedded amd or intel processors.  Here's an example with embedded low end epyc 3101 and dual 10gb.

www.asrockrack.com/.../productdetail.asp

Here's one you can drop a Ryzen3 3000 cpu on which also has dual 10Gb intel nics.  https://www.asrockrack.com/general/productdetail.asp?Model=X570D4I-2T#Specifications

Here's an asus example with dual intel gig. https://www.asus.com/ca-en/Commercial-Servers-Workstations/P10S-I/

None of these are what I would call inexpensive.