In a large Dutch oven or heavy pot over medium heat, melt butter.
Add orzo and garlic and cook, stirring occasionally, until orzo is lightly toasted and garlic is fragrant, about 4 minutes.
Add tomato paste and cook, stirring, until combined, about 1 minute.
Add broth, milk, sun-dried tomatoes, salt, and pepper.
Increase heat to medium-high and bring to a boil.
Reduce to heat to medium-low and simmer, stirring frequently, until liquid is mostly absorbed and orzo is tender, 12 to 14 minutes.
Add spinach and Parmesan and cook, stirring frequently, until spinach is wilted, about 2 minutes.
Remove from heat and season with salt and pepper, if needed.
Top with more Parmesan.
