The phrase "a process that encourages" is correct and usable in written English.
You can use it when describing a method or system that promotes or supports a particular behavior or outcome.
Example: "The workshop is designed as a process that encourages creativity and collaboration among participants."
Alternatives: "a method that fosters" or "a system that promotes".
It is much more useful to see it as a process that encourages reflection.
"[It is] a process that encourages the conversion of socially created anxiety into medical diagnoses suitable for drug treatment.
All the families have climbed what Howard Husock calls the housing ladder, a process that encourages people to acquire bourgeois values instead of hoping to luck into a subsidized home.
As the scholars Jack Goody and Ian Watt observed, it is only in a literate culture that the past's inconsistencies have to be accounted for, a process that encourages skepticism and forces history to diverge from myth.
The method used to produce Époisses is what the French call caillé lactique, in which the curd develops slowly over many hours at low temperatures with very little rennet, a process that encourages the development of both fine flavors and the acidity that helps to inhibit the growth of pathogens.
It's in the conclusion that things get seriously ominous: "As the scholars Jack Goody and Ian Watt observed, it is only in a literate culture that the past's inconsistencies have to be accounted for, a process that encourages skepticism and forces history to diverge from myth".
The idealism and transcendentalism of Romantic thought were challenged by the growing prestige of empirical science and utilitarian moral philosophy, a process that encouraged more-objective modes in literature.
The program brought at-risk kids together to play under rules decided democratically by the players on both teams, a process that encouraged collaboration, peaceful conflict resolution, gender equality, and inclusion.
He later brought this high-level of efficiency to his role at Google, where he launched and spearheaded a new approach called Sprint, a speedy process that encourages teams to hatch an idea and move it from prototype to road-testing in just five days, saving teams time and money.
Until the mid-eighties, the two of them hand-set text on an old letterpress, a laborious process that encourages caution and thrift.
A controlled auction is a sales process that encourages potential buyers to submit offers.
