You'll better take advantage of the many built-in rules of GNU make. Run once make -p to learn them. So you should use CXX instead of CC and replace CC_FLAGS with CXXFLAGS.
You may want to build a statically linked executable. Then you should pass -static into your linking command, using LINKFLAGS
So try with
## untested Makefile for GNU make
# variables known to make
CXX= g++
CXXFLAGS= -std=c++11 -O2 -Wall -Wextra
LINKFLAGS= -static
LIBS= -lpthread -lmicrohttpd -lz
# this project needs:
MYEXEC= cpp_server
MYSOURCES= $(wildcard *.cpp)
MYOBJECTS= $(SOURCES:.cpp=.o)
.PHONY: all clean
all: $(MYEXEC)
$(MYEXEC): $(MYOBJECTS)
$(LINK.cc) $^ $(LOADLIBES) $(LDLIBS) -o $@
clean:
rm -f $(MYEXEC) $(MYOBJECTS)
AFAIK you don't need anything more in your Makefile (provided you use a GNU make, not e.g. a BSD one). Of course you need appropriate TAB characters in your Makefile (so you need to use some editor able to insert them).
You could want to statically link only -lmicrohttpd (and dynamically link the other libraries; however, you might want to also statically link the C++ standard library, which depends upon the compiler and could change when the compiler changes; linking also the C++ library statically is left as an exercise). You could do that with removing the LINKFLAGS line and using
LIBS= -Bstatic -lmicrohttpd -Bdynamic -lz -lpthread
BTW the -shared linker option is need to build from position-independent code object files a shared library (not to use one). See this and that.
You may want to use make --trace (or remake -x, using remake) to debug your Makefile
If you want to understand what actual files are linked, add -v -Wl,--verbose to LINKFLAGS perhaps by running make 'LINKFLAGS=-v -Wl,--verbose' on your terminal.
You might want to make clean before anything else.